For some small part, in a minor show they won't check your background, but for any lead roll in a big TV deal, or a movie they will. Well, not the show, the insurance company that's going to write a completion bond. There is far too much money at stake to take any chances.
And yes, someone could recognize you. Or, on the off chance you make it, the press will start digging.
And acting like modeling and stuff like that - - they don't care about you, as much as they care about how you look on the screen, if you have the look they want, they won't care about other things. But, they do care about PR (a huge amount) and having a trans actor would be good press, I'm sure they would want to make it a publicity item.