No. Facebook strictly limits what can be done with groups, and since groups are generally private, there are a lot of privacy concerns that need to be taken into account when working with groups as well. JFBConnect currently has no support for pushing content to or from groups. It's something we get requests for every few months, but it's not a common request. We may investigate adding group support in the future, but don't have any timeline on when, or if, we may support groups.
Sorry that that's not what you were looking to hear, but hope it explains.
Alex
Live Streaming Groups using JFBCFAN
