Maybe, store it in a pillow case. I've heard the fabric is able to breathe that way.
I'll be anxious to hear what you plan to do with the blocks.
I have an old, old quilt from my husband's side of the family. It was being used as a packing blanket!!!!! I have rescued it although it is very holey and well worn. I plan to take the best area and frame it under glass. The pattern is Drunkard's Path, red and white. It is another UFO and when I get it done, I plan to post pics!