Yeah, I probably would, if I could see that it was clean, and came from a pet/smoke-free home. Because dustmites are a fact of life with natural fibers, I wouldn't worry about two years worth-- would you replace a two-year-old mattress of your own because of dustmites? And around here we don't have to worry about begbugs (yet. shudder).
The thing I would NOT do is steam it. Moisture ruins futons, clumping the cotton fibers together and making them permanently lumpy.
Gotta say, I love the post-consumer gray market, and feel like it's just the most ethical (not to mention cheapest) place to get almost anything!