I would NOT fly with my Martin. I have seen cases that are make to checked, but I would not check a Hardcase, and they may not be willng to store in on board.
I fly a great deal and hve seen some real nightmares.
When I travel I try to find a friend who is willing loan me a guitar, I always bring with new strings.
I also keep a second Guitar at our Condo in Noth Carolina.