The option is a lie, I did this the fall after the Snowden releases, and then this past summer decided to see if the delete actually happened after the two week period that was part of that process then, everything from my account was still there, nothing was deleted.
fwiw I did this and it worked for me. It can take more than two weeks and if you login the process is interrupted. A good bet is to ask your friends when your messages appear as "facebook user". After that my login didn't work anymore.
