Because the terms "man" and "woman" have been socially created, they may mean different things for different people. I would have to say though that "yes," if the person considered themself a woman, then I would accept them as a woman. It's interesting that male DNA doesn't necessarily mean a dominance in male hormones, so that whole situation can get kinda complex.
I've got a fun question for you as well.
If an individual with female DNA, masculine genitalia and a masculine appearance goes in for surgery to become a "woman" are they then a woman?