This is technically possible by creating a new usergroup and auto-adding users based on the birthday user criteria. However, adding a new usergroup means a whole lot of headaches. E.g., more permissions to adjust when creating private/restricted forums, more permissions to adjust when adding new addons, bigger forum permission cache (usergroups x permissions x node), etc.
Perhaps adding a banner for a user based on certain criteria (has birthday, is featured, etc.) would be beneficial to other folks, too.