I agree, call the airline. I know Bonnie Hunter has posted here and there on her blog about traveling with her FW, you might read her experiences.
Years ago I worked at the airport. One of my jobs was loading/unloading the bags from the belly of the plane. Just because it's marked "fragile" does NOT mean it will always be treated as such. Sometimes it is too dark to see. Sometimes the writing is not visible. Sometimes the employee is hurrying, trying to get the job done and doesn't take the time to read the side of the box before grabbing it. Sometimes the employee is a jerk and thinks it's funny to throw fragile items around. It's a crap shoot. If you have to check it, make sure it is packed very securely.