No, they just have to store the fact that you don't want your account to be tagged in other people's photos. Of course that doesn't stop people from tagging as your name (not linked to your account) or a variation of it, but that's a losing battle.

Actually they already allow you to opt out of the facial recognition feature:

"Who sees tag suggestions when photos that look like you are uploaded?" ("Friends" or "No one")

You can also set Facebook to require manual review of friends' tags of you. I'm not sure if there's a way to completely opt out of being tagged though.