I'd click yes. Two reasons:
1. I hate Facebook.
2. Any site dumb enough to have a page that says "Do you want to shut this site down? YES NO" that actually shuts the site down if I click yes deserves to die. So either the button is real and Facebook rightfully dies for being so damn stupid, or it doesn't work and it didn't matter that I clicked yes.
Also, to the people who are going "OMG NO HOW WOULD I KEEP IN TOUCH WITH PEOPLE I DON'T BOTHER TALKING WITH ELSEWHERE HOW COULD YOU SHUT IT DOWN!" Facebook is just one social networking site. There are others, so please scale back the drama. You're acting like Facebook going away would bring about the end of the world as we know it, when in reality all you would do is just sign up for the next site. Remember, MySpace used to be the hip place to have a profile, and now it's about to die. These sites come and go, so if Facebook left, there would just be another to take its place.