At the moment in my Pokémon Mystery Dungeon: Explorers of Sky I am re-playing the Special Episode In the Future of Darkness, featuring Grovyle and Dusknoir. There is an option to take items from my regular story game.
If I use a TM to teach Grovyle a move, will that TM disappear in my main game?
Yes, any items taken from your in-game storage will disappear when used in a Special Episode, which includes teaching Grovyle a TM in this case.
Source: Played and beaten the entire game, including replaying all special episodes.