I don’t know if this is possible at the moment. I started writing a plugin to try and add this functionality but my knowledge of php is not good enough.
I have achieved a similar solution, though it lacks some functionality, by using a multisite wordpress install, and having each site with its own forums, and making each site only viewable to members. Then, if you want a user to be able to see a forum you make them a member of the site. The downside of this is that you have multiple forum areas.
I have created some shortcodes to allow you to list forums from multiple sites on single page, but have not got around to adding it as a plugin yet.