Yes, in that sense it did not have to be absolutely positively Mary. She was a normal young girl, and simply chosen by God. However, I don't think it could have been "anyone" else because prophecy considerations still had to be met.
In addition, God COULD have "made a copy" of someone's DNA who was in the line of David, and then zapped that baby into Mary, but I just think that sounds less genuine. That also raises the "conceive" issue.
I agree with your assessment. It had to be someone from the line of David. In which case, the "zapping" part wouldn't have worked either. Zapping implies that her blood has nothing to do with the child. Christ had to have David's bloodline running through His veins.