Assuming that you mean sexual miscreant by pervert, then yes, there's probably someone bold enough to do it. My thought is that someone who is trans and bold enough to switch restrooms in public - they're probably passible enough and not looking for conflict...
Who needs to get busted? The chick who's got a crew cut and is (ahem)packing walking into the mens room or the creepy dude with three-day stubble and a Goodwill dress? There's enough laws to be able to address this situation.
So, dumb law? Maybe. Beneficial in 'protecting our children'? Doubtful Will enrage the queer community? Most certainly.
Agreed.