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I would think the OSB would draw a lot more moisture and perhaps swell. Maybe you could use the newer, treated OSB that's supposed to resist taking on moisture and swelling. I think the idea is that you don't need to Tyvek the place if you use the coated OSB, but I could be wrong.
Coat plywood, OSB, whatever......with "WATER BASE" Polyurethane, and not only will there be no moisture absorbtion, but no odor as well.