Some DZ's have rules against it. Mostly cause it's typically going the other way, male instructor trying to sleep with impressionable girl students.
Also, heh - reality check here. If you're a dude, in an AFF class, with almost no jumping experience and no time around the sport - you are gonna have to be exceptionally amazing as a person in personality, looks or both to get her attention.
It's like 2:1 dudes to chicks (or worse) on a dropzone, she likely has more attention than she knows what to do with.
That said, hey - you never know if you don't ask right?