Yes, your disposables will get damaged. As all checked bags have to be xrayed, and the xray is more powerful than what you go through at security. You may not notice the damage, or you may have totally fogged pictures. I believe you can have the disposables developed on the ship. I could be wrong.
All film will suffer from xray exposure, the faster the speed, the more likely you will notice it, even going through security. An the more times the film goes through, the worse the damage gets. Either have your film hand screened, or try to limit the trips it takes through the xray.