Does Catholic doctrine teach that the Incarnation would have taken place regardless of Adam's decision?

St Thomas Aquinas asks in Summa Theologica 3.1.3, "If man had not sinned, would God nevertheless have become incarnate?" (Latin: Si h*m* non peccasset, nihilominus Deus incarnatum fuisset?). His answer is "no", while acknowledging that God could have still chosen to become incarnate for other reasons; although he recognizes a diversity of thought on the issue, and his opinion should probably be taken as trying to be persuasive more than definitive.

His patristic authority is a sermon of St Augustine (numbered 174 in Migne's Patrologia Latina vol. 38, col. 939ff, and also known as Sermon 8 De Verbis Apostoli). He says on 1 Timothy 1:15 (sermon chapter 2),

If man had not perished, the Son of man would not have come. Because man did perish, the God-man came, and man is found. Man died by free will: the God-man came by liberating grace.

Si h*m* non perisset, Filius hominis non venisset. Ergo perierat h*m*, venit Deus h*m*, et inventus est h*m*. Perierat h*m* per liberam voluntatem: venit Deus h*m* per gratiam liberatricem.

and then later in the same sermon (chapter 7),

There was no other reason why he would come into the world.

Alia causa non fuit quare veniret in mundum.

This assertion is explored through the metaphor of sickness; the healthy do not need a doctor (cf. Matthew 9:12, Mark 2:17, Luke 5:31).

Thomas also considers whether some form of Incarnation might have been desirable even for un-fallen humanity, in order to bring human nature closer to the divine. He does not object to the idea, but he wishes to make it clear that this, as an act of grace, is not inevitable (in the sense that the imperfection of merely human nature demands action on God's part). The fact that it did happen for fallen humanity, even in accordance with God's foreknowledge and predestination, doesn't stop it from being a free gift.

I think the thrust of your question is about the implications for Christology. Orthodox Trinitarianism insists that the Trinity is a correct description of the way that God is (as otherwise the work of Christ in revealing God to us is flawed) and always has been (the nature of God is not contingent on created things, including time). The Son is meant to be eternally begotten of the Father. But the Incarnation is not part of the essential nature of God, as that would make God ontologically dependent on part of his creation - us. This relates to the fourth-century debate over the nature of the relationship between Father and Son, as a result of which the Nicene-Chalcedonian formulation of the faith came to distinguish between the Son being begotten but not created. So the Tome of Pope St Leo the Great, received at Chalcedon, says:

When God is believed to be both almighty and Father, the Son is clearly proved to be co-eternal with him, in no way different from the Father, since he was born God from God, almighty from the Almighty, co-eternal from the Eternal, not later in time, not lower in power, not unlike in glory, not distinct in being. The same eternal, only-begotten of the eternal begetter was born of the holy Spirit and the virgin Mary. His birth in time in no way subtracts from or adds to that divine and eternal birth of his: but its whole purpose is to restore humanity, who had been deceived, so that it might defeat death and, by its power, destroy the devil who held the power of death.

Therefore, we can believe at the same time:

1. The Incarnation was predestined (as in Jerome's translation of Romans 1:4, praedestinatus est) from the beginning of time.
2. The Son's relationship to the Father is, and always has been, one of being "begotten".
3. The Incarnation was an act of grace, that was not caused or merited by us, but depends only on the free action of God himself.
4. The fact of the Incarnation does not make the Son's son-ship or begotten-ness logically dependent on us. The unincarnate Word is still the Word.

Consequently, whether we sinned or not, the Incarnation was not "forced" on God (i.e., he does not have to become incarnate in order to be true to his own triune nature). If we had not sinned, then the Incarnation would not have been needed in order to conquer sin. It could still have happened for another reason, as Thomas says: "For God would have been able to become incarnate, even if sin did not exist" (potuisset enim, etiam peccato non existente, Deus incarnari). And further (ST 3.1.1 ad 1), "The mystery of Incarnation was not completed through God being changed in any way from the state in which He had been from eternity, but through His having united Himself to the creature in a new way, or rather through having united it to Himself" (incarnationis mysterium non est impletum per hoc quod Deus sit aliquo modo a suo statu immutatus in quo ab aeterno non fuit, sed per hoc quod novo modo creaturae se univit, vel potius eam sibi).