Covered storage always helps with moisture. If you go to eastern Oregon or Washington during the winter you won't find an available covered storage space available anyplace. You want to keep the water from falling on it, sitting on it, draining down the sides and so forth. Take covered storage if you can find it.
You could certainly do without the moist air, but there's no way to get away from that except to put it in climate controlled inside storage.
When you say the plywood was damaged, how was it damaged? Was it the structural plywood, inside plywood, or was the outside made of plywood? Covered storage will take care of the water on the outside or leaking into the structure. If you can find a covered place with electrical power to power a humidifier, that would be your best option. Run the humidifier down a sink drain if you don't have to worry about the sink trap or holding tank freezing. There's desiccant and other things, but I've never seen them really work in a larger RV.
Bill