I have used my die cut machine to cut a Lot of fleece in my day. It cuts wonderfully with nice crisp edges. I'd say go for it. The fleece rags will not fray, but they will give a lot of great texture to the quilt. If you use fleece for the backing, I doubt batting will be necessary. A double layer of fleece is really warm, and depending on your batting choice, the batting may shrink with washing. Good luck with your quilt. Making a memory quilt for someone else is sometimes a little nerve wracking, but they so appreciate your endeavors.