Reportedly Norelli concludes that the Vision of Isaiah records a "birth" narrative regarding Jesus that was also known to the writer of Matthew, and that both Matthew and Vision of Isaiah are independent witnesses to this source.
I would add Luke to that as well. I'm not sure why Norelli doesn't. I can only assume it is because Luke's genealogy does not run through Mary, but rather Joseph.
However, if we compare the "birth" story in VoI to Luke, however, it seems quite apparent that canonical Luke is responding to the account in VoI.
2. And I indeed saw a woman of the family of David the prophet, named Mary, and Virgin, and she was espoused to a man named Joseph, a carpenter, and he also was of the seed and family of the righteous David of Bethlehem Judah.
3. And he came into his lot. And when she was espoused, she was found with child, and Joseph the carpenter was desirous to put her away.
4. But the angel of the Spirit appeared in this world, and after that Joseph did not put her away, but kept Mary and did not reveal this matter to any one.
5. And he did not approach Mary, but kept her as a holy virgin, though with child.
6. And he did not live with her for two months.
7. And after two months of days while Joseph was in his house, and Mary his wife, but both alone.
8. It came to pass that when they were alone that Mary straight-way looked with her eyes and saw a small babe, and she was astonished.
9. And after she had been astonished, her womb was found as formerly before she had conceived.
10. And when her husband Joseph said unto her: "What has astonished thee?" his eyes were opened and he saw the infant and praised God, because into his portion God had come.
11. And a voice came to them: "Tell this vision to no one."
12. And the story regarding the infant was noised broad in Bethlehem.
13. Some said: "The Virgin Mary hath borne a child, before she was married two months."
14. And many said: "She has not borne a child, nor has a midwife gone up (to her), nor have we heard the cries of (labour) pains." And they were all blinded respecting Him and they all knew regarding Him, though they knew not whence He was.
15. And they took Him, and went to Nazareth in Galilee.
16. And I saw, O Hezekiah and Josab my son, and I declare to the other prophets also who are standing by, that (this) hath escaped all the heavens and all the princes and all the gods of this world.
17. And I saw: In Nazareth He sucked the breast as a babe and as is customary in order that He might not be recognized.
3. And he came into his lot. And when she was espoused, she was found with child, and Joseph the carpenter was desirous to put her away.
4. But the angel of the Spirit appeared in this world, and after that Joseph did not put her away, but kept Mary and did not reveal this matter to any one.
5. And he did not approach Mary, but kept her as a holy virgin, though with child.
6. And he did not live with her for two months.
7. And after two months of days while Joseph was in his house, and Mary his wife, but both alone.
8. It came to pass that when they were alone that Mary straight-way looked with her eyes and saw a small babe, and she was astonished.
9. And after she had been astonished, her womb was found as formerly before she had conceived.
10. And when her husband Joseph said unto her: "What has astonished thee?" his eyes were opened and he saw the infant and praised God, because into his portion God had come.
11. And a voice came to them: "Tell this vision to no one."
12. And the story regarding the infant was noised broad in Bethlehem.
13. Some said: "The Virgin Mary hath borne a child, before she was married two months."
14. And many said: "She has not borne a child, nor has a midwife gone up (to her), nor have we heard the cries of (labour) pains." And they were all blinded respecting Him and they all knew regarding Him, though they knew not whence He was.
15. And they took Him, and went to Nazareth in Galilee.
16. And I saw, O Hezekiah and Josab my son, and I declare to the other prophets also who are standing by, that (this) hath escaped all the heavens and all the princes and all the gods of this world.
17. And I saw: In Nazareth He sucked the breast as a babe and as is customary in order that He might not be recognized.
Compare to Luke:
Luke 1:
39 Now at this time Mary arose and went in a hurry to the hill country, to a city of Judah, 40 and entered the house of Zacharias and greeted Elizabeth. 41 When Elizabeth heard Mary’s greeting, the baby leaped in her womb; and Elizabeth was filled with the Holy Spirit. 42 And she cried out with a loud voice and said, “Blessed are you among women, and blessed is the fruit of your womb! 43 And how has it happened to me, that the mother of my Lord would come to me? 44 For behold, when the sound of your greeting reached my ears, the baby leaped in my womb for joy. 45 And blessed is she who believed that there would be a fulfillment of what had been spoken to her by the Lord.”
...
Luke 2:
4 Joseph also went up from Galilee, from the city of Nazareth, to Judea, to the city of David which is called Bethlehem, because he was of the house and family of David, 5 in order to register along with Mary, who was engaged to him, and was with child. 6 While they were there, the days were completed for her to give birth. 7 And she gave birth to her firstborn son; and she wrapped Him in cloths, and laid Him in a manger, because there was no room for them in the inn.
8 In the same region there were some shepherds staying out in the fields and keeping watch over their flock by night. 9 And an angel of the Lord suddenly stood before them, and the glory of the Lord shone around them; and they were terribly frightened. 10 But the angel said to them, “Do not be afraid; for behold, I bring you good news of great joy which will be for all the people; 11 for today in the city of David there has been born for you a Savior, who is Christ the Lord. 12 This will be a sign for you: you will find a baby wrapped in cloths and lying in a manger.” 13 And suddenly there appeared with the angel a multitude of the heavenly host praising God and saying,
14 “Glory to God in the highest,
And on earth peace among men with whom He is pleased.”
15 When the angels had gone away from them into heaven, the shepherds began saying to one another, “Let us go straight to Bethlehem then, and see this thing that has happened which the Lord has made known to us.” 16 So they came in a hurry and found their way to Mary and Joseph, and the baby as He lay in the manger. 17 When they had seen this, they made known the statement which had been told them about this Child. 18 And all who heard it wondered at the things which were told them by the shepherds. 19 But Mary treasured all these things, pondering them in her heart. 20 The shepherds went back, glorifying and praising God for all that they had heard and seen, just as had been told them.
21 And when eight days had passed, before His circumcision, His name was then called Jesus, the name given by the angel before He was conceived in the womb.
22 And when the days for their purification according to the law of Moses were completed, they brought Him up to Jerusalem to present Him to the Lord 23 (as it is written in the Law of the Lord, “Every firstborn male that opens the womb shall be called holy to the Lord”), 24 and to offer a sacrifice according to what was said in the Law of the Lord, “A pair of turtledoves or two young pigeons.”
39 Now at this time Mary arose and went in a hurry to the hill country, to a city of Judah, 40 and entered the house of Zacharias and greeted Elizabeth. 41 When Elizabeth heard Mary’s greeting, the baby leaped in her womb; and Elizabeth was filled with the Holy Spirit. 42 And she cried out with a loud voice and said, “Blessed are you among women, and blessed is the fruit of your womb! 43 And how has it happened to me, that the mother of my Lord would come to me? 44 For behold, when the sound of your greeting reached my ears, the baby leaped in my womb for joy. 45 And blessed is she who believed that there would be a fulfillment of what had been spoken to her by the Lord.”
...
Luke 2:
4 Joseph also went up from Galilee, from the city of Nazareth, to Judea, to the city of David which is called Bethlehem, because he was of the house and family of David, 5 in order to register along with Mary, who was engaged to him, and was with child. 6 While they were there, the days were completed for her to give birth. 7 And she gave birth to her firstborn son; and she wrapped Him in cloths, and laid Him in a manger, because there was no room for them in the inn.
8 In the same region there were some shepherds staying out in the fields and keeping watch over their flock by night. 9 And an angel of the Lord suddenly stood before them, and the glory of the Lord shone around them; and they were terribly frightened. 10 But the angel said to them, “Do not be afraid; for behold, I bring you good news of great joy which will be for all the people; 11 for today in the city of David there has been born for you a Savior, who is Christ the Lord. 12 This will be a sign for you: you will find a baby wrapped in cloths and lying in a manger.” 13 And suddenly there appeared with the angel a multitude of the heavenly host praising God and saying,
14 “Glory to God in the highest,
And on earth peace among men with whom He is pleased.”
15 When the angels had gone away from them into heaven, the shepherds began saying to one another, “Let us go straight to Bethlehem then, and see this thing that has happened which the Lord has made known to us.” 16 So they came in a hurry and found their way to Mary and Joseph, and the baby as He lay in the manger. 17 When they had seen this, they made known the statement which had been told them about this Child. 18 And all who heard it wondered at the things which were told them by the shepherds. 19 But Mary treasured all these things, pondering them in her heart. 20 The shepherds went back, glorifying and praising God for all that they had heard and seen, just as had been told them.
21 And when eight days had passed, before His circumcision, His name was then called Jesus, the name given by the angel before He was conceived in the womb.
22 And when the days for their purification according to the law of Moses were completed, they brought Him up to Jerusalem to present Him to the Lord 23 (as it is written in the Law of the Lord, “Every firstborn male that opens the womb shall be called holy to the Lord”), 24 and to offer a sacrifice according to what was said in the Law of the Lord, “A pair of turtledoves or two young pigeons.”
So, in VoI we are told that Mary was never pregnant and the baby was never in her womb. We are told that she did not give birth, rather the child just appeared. The "appearance" of Jesus was unannounced and his identity remained secret.
Luke counters each of these points specifically. In Luke, we have a witness to the pregnancy of Mary in the mother of John. We are told explicitly that the child was in her womb. We are told explicitly that she gave birth. The birth of Jesus is announced immediately for all to know, including all of the powers of this world.
So, regardless of whether this narrative was known to Matthew and Luke from its current context or not, they both knew this narrative and were independently responding to it.
I think this best explains the similarities and differences between the birth stories of Matthew and Luke. They are both strikingly similar, yet have key differences. But their similarities can be explained by independent use of this narrative.