You'd be better off with something like tineye or google image search; something that snarfs all the photos off the web, you know, does this regularly and timestamps where it saw the photo first. It wouldn't be 100% but would likely work better than the cooperative solution you propose, and it's something that is well within the capabilities of facebook.
Even then... yeah, I think this sort of thing is going to be pretty much impossible to completely stamp out as long as you can sell fake profiles for enough money that you can pay an actual human to create them.
Also images uploaded on Facebook aren't public by default, so tinyeye etc wouldn't have them.
Of course it's not fully thought out how it would work, maybe just for people who are new to FB? You also need some sensible image recognition algo, or you'll get a lot of chopped off head mashes. But I'm sure FB has staff for that sort of thing.