A simple and good question asked by a curious person around the process of transitioning, my response in a nut shell:
No it doesn't in this instance...
If I was staying female I imagine it probably would unless one started HRT as it's true I no longer have ovaries producing estrogen in the body, however taking testosterone regularly and having the normal level of this hormone (around 25) circulating through my system, voids that from happening.
On a more esoteric note, we all have a body and have the capacity to shift how we live within the context of the word 'gender'. A significant proportion of the world population have a fixation to their gender and exist in its behavioural confines quite happily, others set out to influence and change the societal gender norms to what they feel it should be, while others just go ahead change their gender entirely to align within a deeper knowing that they are more than (different than) what their sex organs suggest.
My body did have a female operating system with sex organs and estrogen as the major hormone influence (giving the female appearance), every person's body has both hormones (just differing levels). Now that I've removed the sex organs that give the appearance of a female and given the body testosterone consistently, it takes on the male appearance and bodily functions, voiding any female operating system issues like menopause when you stop estrogen.