I did the very same thing with a quilt my mother had made. She had used a sheet for the backing and it kind of just dry rotted! I tore off as much of the sheet, which was in shreds, as I could easily. Then, leavng the rest of the sheet and batting, I backed it and quilted it with stitch in the ditch. I didn't add more batting, but it would have worked just fine if I had. Go for it...!