I've done a fair amount of work with facebook pages, and know alot of people in the various Episcopal church related sites doing this as well. One thing to be aware of, though is that facebook has changed its "group" feature, so you cannot make new groups with discussion boards. The old one's continue to exist, but new one's default to a new groups feature-- which instead of boards acts more like a super-wall with topics there instead. Its workable, but a lot less neat and alot of people I know are frustrated with the change. The new option does not allow mass-messages to members, but does default to notifying members when ANY new activity happens in the site... which can be tweeked down, but gets very annoying if someone does not understand when they join and may lead to abandoning any activity. Someone wanting to try out this feature would be wise to post info on the profile advising people how the settings work so they can customize without shutting off notifications completely out of annoyance (my recommendation would be to limit it to "new topics" and "replies to discussions you are in").
The group option does still have the option of being public, semi-private (all people can see group, but only members can read/post comments), and secret, which is useful in weeding out spammers or allowing more frank discussions that aren't all over the internet.
Happy to help out or look for more resources with this. The new system is workable, but you should be aware of these major changes that have done away with the boards and some of the other nice features of the old groups.