In regards to Catholicism, there’s a difference of opinions when you start talking to religious orders and theologians. Such as Dominicans believe that he wouldn’t have come based on St. Aquinas observations in his
Summa, Tertia Pars Question 1 Article 3. Franciscans believe that he would have come regardless of the Fall, based on the works of Bl. John Duns Scotus.
Our Catechism points to very fine points,
here. Paragrapghs 456-460. Though we acknowledge here He became flesh to save us we also acknowledge He became flesh “so that thus we might know God’s love”, “to be our model of holiness”, and to make us “partakers of the divine nature”. And if we hadn’t sinned, these points would still stand.
The question really boils down to, the Absolute Primacy of Christ. What is the primary reason why the Word became flesh? I fully believe the primary reason is for us to partake of the divine nature, thus He would’ve became flesh regardless of the Fall. But as I have always said, contemplation of possible worlds is incoherent due to the fact we live in the best possible world willed by God.
I made a thread about this a while ago,
forums.catholic-questions.org/showthread.php?t=593556 , had great replies might want to check that up.
A great article about the Absolute Primacy of Christ
irishanddangerous.blogspot.com/2007/04/franciscan-scotistic-thesis-absolute.html
A great youtube series of the Absolute Primacy of Christ
youtube.com/watch?v=PX9jEyK5s6E&feature=relmfu at least 30 seperate videos about this. Highly advised, please watch it.