Generally, no; if one represents as binary gender “woman” with subgroup “trans”, it is implied and understood that they are not a member of binary gender “man”. That they are a member of subgroup “trans” is not relevant to resolving their binary gender either-or, in your example.

They might be “male at birth” or “intersex at birth” on certain medical paperwork, and those physical sex characteristic will remain unchanged in subgroup “at birth” regardless of any shift in gender or medical alterations to their present-day sex characteristics.

(To avoid any possible confusion, I’m keeping in mind that “male” is sex and “man” is gender, as this is often confused in discussion of these topics. One’s sex is a physical characteristic like one’s eye color or skin tone; most people assume that everyone has just one and that it doesn’t change, neither of which are true. One’s gender is a behavioral characteristic like accent or musical tastes; it can’t be reliably guessed from any physical characteristic, and it can change at any time, either gradually over years or all at once at a coffee shop or anywhere in between.)