>>52127840No, Anon, theres 2 Koraidons. The first one, that you ride throughout the game is obtained for use in battle exactly as I described, and like the starter in LGPE you can't trade, box, or release it.
The second Koraidon can be found in the postgame in the final area, you are free to battle and catch it and then do what will with it like any other pokemon.