David,
Short answer, yes, the human nature assumed by Our Lord was as pure and as spotless as was Adam's before the fall.
Let's review a few vital points.
Sin is not essential to the human nature qua nature (qua - in the capacity of, as being). Sin is not some ontological entity, existing by itself. Sin relates to a law that has not been obeyed. Sin therefore is a moral act. The corruption of a Person is not a material corruption, it is a moral corruption.
Our Lord Jesus Christ was not two somethings existing side-by-side in one person. Jesus Christ was a divine person, a person Who assumed a human nature. That human nature so taken up was consecrated (kept pure and spotless) and specifically created by the miracle and agency of God the Holy Spirit (Luke 1:35). That human nature was an impersonal human nature.
Calvin is instructive here (emphasis mine):
"Christ was not free of all taint, merely because he was born of a woman unconnected with a man, but because he was sanctified by the Spirit, so that the generation was pure and spotless, such as it would have been before Adam’s fall." (Inst. 2.13.4).
If you wrongly try to abstract the human nature of Jesus away from God incarnate you ignore the plain fact that persons sin, not natures.
The human nature of Jesus Christ only existed in union with the divine Person, the Second Person of the Trinity. Given this union, there is no possibility that the Person, Jesus Christ, could sin. Why? His divine nature—not some donum superadditum (super added gift of grace)—made the possibility of sin impossible.