Wouldn't that just increase the problem that the person you are responding to brought up? If you capture their facial movements, it might be even easier to tell if they are a man or a woman, despite any scrambling you do.
Yes. If the goal is gender blindness, a more effective strategy is to block all video and voice communication. Even chat could be a giveaway. Go off of nothing but code against a test suite.
Quite possibly! That's the extra dimension added to the experiment. :)
It would be even more fascinating if you could cluster facial expressions or motions as "more female" or "more male". And for bonus points, work out a way to "filter" or "smooth" the facial signal to reduce/remove these giveaway hints (or insert false hints).