Access Levels and BuddyPress Groups

Can a change in Access Levels change a BuddyPress group automatically?

What'd I'd like is to be able to assign a member to an Access Level and have them removed from one group and added to another in BuddyPress - or vise versa.

When I put the BuddyPress / Groups rule into an Access Level, there are none of the existing Groups listed. Is this what this rule is for, or am I misunderstanding?

Thanks!