Yes, you'll still need badges to get them to obey you. Your Honedge will likely alternate between ignoring you (obedience issue) and hanging in there for you/gaining Amie benefits, but it won't obey all the time. One solution is to breed a Honedge on one game and then trade it to the other game. If you can only move Pokemon via Bank, you could get help from someone here so you can move the egg over from one game to the other via trading. Then hatch the egg, and you'll have an obedient Honedge with your OT.