Whenever Q is the first Pokémon in the party, all of the Pokémon below it will be invisible, because it is treated as the cancel button. The party will then be unable to be healed at any Pokémon Center and can only be healed via items. If Q is moved to the bottom of the party, all other Pokémon will once again be visible and will be able to be healed at a Pokémon Center. Once Q faints, it can only be healed by using a Revive or similar item.
Q glitch
Due to Q's unusual behavior, it and its Red and Blue equivalent Charizard 'M are the only glitch Pokémon which enable a player to trigger the Q glitch. It involves depositing Q and other Pokémon into Bill's PC in a certain order, and then when they are retrieved, the Pokémon's attacks and stats will be transferred from one Pokémon to another.
This glitch Pokémon article is part of Project GlitchDex, a Bulbapedia project that aims to write comprehensive articles on glitches in the Pokémon games.