tmagann:
You can't block Group 0. Everyone, even those not in the game can see it.
Worth noting that this is not actually 100% accurate. (Or at least it didn't use to be as recent as last year.)
Anyone that isn't a member of your game, or isn't actively logged in to RPoL, CAN always see Group 0...
BUT...
players in your game that are logged in to their character in your game will be unable to see Group 0 unless their character has Group 0 access.
tl;dr: You can remove Group 0 access from a player that has been added to your game.