In a sense it would. But only if you define what you mean as "The Incarnate Christ". The Nestorians of the time would have agreed with that statement, even though they have a radically different view of what the Incarnation is than most Christians. They believed that Jesus was a divided man, in effect two people. That is what the Incarnation meant to them. It was one of the titles suggested (or something close), but was not chosen because it wasn't explicit enough.
I think it would, however, put the emphasis more on the person of Christ; however, than the person of Mary. To be the Mother of the Incarnate Christ doesn't neccessitate that she pre-exists before God. One would then concentrate on what happened at the incarnation. Christ became BOTH God and Man, a 100%/100% person in complete unity and yet distinct in the fact that his Godhood preexisted eternally, whereas his manhood had a beginning.