Every user is automatically included in a "User Group" corresponding to their WordPress blog role.  I call this a WP Role metagroup.  These groups are named [WP Subscriber], [WP Contributor], etc.  They do not appear in the administrative listing of WP Admin > Groups, as you cannot manually edit them or add members to them.  But in any User's profile, the metagroup will appear alongside any manually assigned groups.

There is not currently any facility to automatically add new users to a custom User Group which they could subsequently be manually removed from.  Would you see an advantage to doing that?