Would using huge materia as a sort of explosive material drain the planet of energy in the same way as when a person uses the materia? I don't remember the game telling me (or the party) that simply using already existing materia would damage the planet. Is this something that was lost in translation?

Even if it does, the options at that point in the game are either allow meteor to crash down and definitely completely smurf up the planet, or use huge materia to blow it up even if this bears the risk of damaging the planet. It could still be the lesser of two evils to use the huge materia, and Cloud & Co. wrecks this plan for no good reason except "shinra's doing it and we hate them", with no regard the results of their actions.