Yes you are definitely going to need to check it. If they're preventing people from getting on board airplanes with fingernail clippers, the Iaito is not gonna make it on.
Your best bet is a hardened gun case. The kind with the tough plastic exterior. This isn't the cheapest option however. There are some hard plastic fishing rod carriers that would also work as long as you filled them with padding to take up the extra space.
You can also use a length of 4 inch pvc pipe. Just make sure you load the bottom with padding and wrap some padding around the Iaito so it doesn't bang around inside the tube. Seal one end with a 4 inch flat cap. There are screw caps available at most hardware stores that would screw on to the other end. This makes for a pretty tough carrying case, but unless you put some kind of carrying strap on it, it's a bit akward.
They shouldn't give you too much grief as long as you check it in with the rest of the baggage. I'm sure you'll get other advice here as well.
Charles Mahan
Iaido - Breaking down bad habits,
and building new ones.