BuddyPress.org

I’ve been considering the same thing. In my research here’s the list of plugins I needed to still evaluate. Not a perfect plugin I think for this, but one of these plugins should be able to easily be modified to do what you want if you know a little PHP and WP/BP. Otherwise, I’m planning to dive into it myself over the next couple months. I hope these links help:

https://buddypress.org/forums/topic/join-all-public-groups-at-once

https://wordpress.org/extend/plugins/auto-join-groups/

http://buddypress.webdevstudios.com/blog/2009/11/13/buddypress-registration-options/

I also had the welcome pack on my list since it does make sense to have this part of it also.