I just moved this to the #feature:voting category as I'd like it to be thrown into the mix for voting when that starts happening.
I like this idea! There is one person in charge of managing internal groups in my community but does not need to have admin privileges. It would be helpful to be able to set up a group for this so we can easily add/remove people to help her.
Another related feature that would be needed is the ability for group owners to see and manage the group even when "Group is visible to all users" is deselected. There should also be the option to allow group members, or members of a specific other group, to see the group.