You can use a blank TM to obtain a TM version of any move one of your pokemon have. That doesn't necessarily mean it can be taught to anything, they would have to decide on a learnset for it, but you can get it in TM form.
Not changing this sig until we get a new main series Tales game released on a Nintendo console in the US
How about it teaches Egg Moves, Move Tutor moves (from all generations the Pokémon existed in), TM moves (from other generations that the Pokémon was in), and Dream World moves? That gives them some pre-existing lists to check the moves against. CONTRARY SUPERPOWER SPINDA!
For those of you starting topics about the PS4, there's a PS4 board: http://www.gamefaqs.com/boards/691087-playstation-4