Actually, ok, it doesn't go through Facebook. You just get email notifications. Drat! I'm trying to migrate this huge group of people off of this Facebook forum, but Facebook is useful as a centralized way to get notifications. Back to looking at Wordpress...
Oh, weird. Well, it was really helpful, because when I first wrote this post, I actually didn't get Facebook notifications. But now I do, I guess, which is great. Handy that Facebook is so connected to everything now.
You would have to create a plugin. That plugin would the forum owner require to create a facebook app so that he can use its API. Then you would have to hook into the notifications API. User must be allowed to not only select being notified with popups and mails, but also with Facebook.