You might be able to use it as a backing if you quilt it on a frame, but i just don't know. I did use a piece of cotton jersey (meant for apparel) as a backing for a quilt, but quilted it on a frame. It came out very well.
But a jersey sheet stretches so much more than the apparel jersey did, that I won't even hazard a guess about how well it will work, even on a frame.