I've got UFOs stored in one of those zippered plastic bags from the bed in a bag. I doubt that it is airtight with the cloth zipper. IMHO, I think the problem with storing in plastic is if the environment is humid. The contents could mildew. We've got a central unit that is either running on AC or heat, so I think my fabric is safe.
I too used the large ziplocs to keep the tidbits and pieces leftover from the UFOs. But I've already been guilty of using up yardage that was pinpointed for binding. Yikes.