It's an interesting thought experiment. Even if a man could replace every cell in their body, would they really be a woman?
It's not something that's likely to ever be realistic, but I suspect that male socialisation would still set them aside. You couldn't just relive your life.
It'll be interesting to see if they have people treating The Doctor differently in female form.
Realistically she'd lose respect in most cultures on earth, I wonder if the (fictional) universe is inherently sexist too?