I haven't personally used a sheet for backing, but my quilting buddy does it all the time and has had no problems at all. She hits the Goodwill near her home and buys high quality sheets for a few dollars. The trick to using a sheet is the same as buying fabrics, don't buy anything that looks or feels cheap.
ps - 100% cotton will pill just as bad as a blend. Trust me, I threw away 800 count Egyptian Cotton sheets after three washings because they had pilling, or as I like to call them - dingle-berries.