Probably not. JFBConnect can show the stream from a Facebook Group, and allow you (the admin) to easily post content from your site back to it. However, JFBConnect can't selectively show the stream to users without using the ACL permissions of Joomla itself. So, if you will have user's login to your site (using social networks or Joomla itself) and then assigning them to a 'private' group on your site that you want to see your Group feed, then JFBConnect should work for you.
I hope that helps explain, but if not, or you have other questions, just let me know.
Thanks,
Alex