I think it will work fine, but, as suggested by prism99, consider that the wood has acid and take appropriate action.
I have a china closet with glass in my garage that I use to store fabric. The shelves are glass, too. I put a fabric I don't love over the glass to keep the sun out, as my DH tends to leave the garage open and the afternoon sun shines in. I also use two pieces of a 3 piece entertainment center in the garage that have glass, and the glass is covered in the same way. Opening up the glass doors makes it real easy to spot fabric, too.