Since so many states are offering gender neutral license might as well take of advantage of any benefits...
Technically no because it's not exactly a lady. In fact, if I owned a bar, I'd double my prices and then say 50% off for men and free drinks for ladies. That'll teach them.
I don't actually see a purpose of having gender on your license in general. If you get arrested and have a rod a tackle you're going into the male holding area even if you appear to be a woman. They'll figure out your gender when you're getting patted down. The one caveat is getting searched at a stop. Your DL gender is the source of truth for whether you get a male or female officer to pat you down. So there is some utility in terms of avoiding sexual harassment allegations.
The benefit is one more Avenue for the radical left to gaslight people, especially the young people, into thinking gender is a social construct. Other than that there is no benefit and much harm done to society. Nothing innocent about radical leftism.