No you don't have to unless it's group policy that Admins and Super Admins play Team Matches or Vote Chess. When I was Super Admin of Theoretical Novelties, I never actively participated in the group's matches. So unless the group has a rule that all Admins play, then I wouldn't be too concerned. 
-Mark
When you are the leader of a group, do you have to participate in the Team Matches (I don't play Online Chess)?