For sure during the initial installation of the Facebook app you have the option of having your phone sync with your Facebook calendar so any events you confirm your attendance for show up on your BB. Otherwise, I think it's an option you can enable from the app itself.
From my experiece, only new invitations will show up on your BB calendar once you confirm them. The notification has to come through to your device. If you RSVP to an event let's say on your PC, it will not show up on your device.
If you use Google Sync, I find it easier to just import my Facebook calendar into Google Calendar, which then syncs with my Blackberry. It works well and it doesn't depend on the Facebook app at all.