My concern with any sort of significant integration of any sort of group add-on would be that they could give off an exclusive vibe, whereas we want the community here to be as inclusive as possible.
As it stands, everyone on the forum is a member of the same group, without borders or barriers. If groups are able to have discussion boards and such that are private to that group I fear that it would serve largely to fracture the community as a whole into bite-size bits, with the potential for explosive results when such a group somehow feels slighted in one way or another.
While it may seem that my reservations are a result of unfounded paranoia, we have actually experienced such an event here in the past - when we closed our on-site chat room. For our more recent members (and/or those that are unaware, or that may have simply forgotten), we used to play host to a forum integrated IP.Chat system. The chat room was fairly popular, and had about two dozen regulars that would frequent the room quite a bit, to the point that many of them stopped posting on the public forum almost completely in favor of their relatively tight-knit chat room. Eventually we shut down the IP.Chat due to a number of issues we were having with it, which caused a lot of folks in the chat group to go a wee bit atomic, because it was taken as a personal strike against the whole lot of them. Personally, I'd rather avoid a similar situation from being repeated.
In addition to that... is there really any reason to keep any posts at all hidden behind locked doors like that? It would be to no gain to the community as a whole if quality discussions became something locked away in secrecy, unseen by anyone.
At any rate, speaking solely for myself, I don't mind the idea of group systems of a sort being implemented, but I would be completely and utterly against having private boards for them. If anything, I'd think them best suited to being a means by which people with common interests could find each other, such as an 'Blueblood is best pony!' group for aspiring fans of our favorite Equestrian prince.