What is the MOD for "helicopter rescuer" and do they have that in the Marine Corp?

There is no MOS. It would be the crew chief or other crewman. A crew chief is almost always ( I never knew anyone who wasn't) a mechanic. In combat areas another crewman will be igned. He will be any air wing maintenance MOS like metalsmith, hydraulicsman, electrician, comm/Nav technician. Remember, all marines are proficient with weapons. The crew will have a training schedule which includes rescue. All marines are already trained in water survival. Each helo squadron will be igned SAR (search and rescue) duties. You just go do your job, you don't need a lot of additional training.