Ya mon, no problem with the hard cooler(as long as it has wheels and a handle for pulling).
You just have make sure it's secure and they can open it and secure it again as it goes as checked luggage. The first year we duct taped it shut and put a half a roll in the cooler for them to tape it back up with. The second time I had a couple of one inch wide nylon straps that we used. When we got to JA it was ok but one of the straps had broke...So next time it's back to the duct tape. Oh, and you will more than likely have to go through the "declare" line as they will want to have a look inside, at least I had to
