MisDixie

Yes cotton will fray as will any fabric that is woven. I have made demin rags with drapary fabric samples and a cotton back. Turned out lovely. I have also done demin rag mixed with flannel on the front, memory quilts for freinds made with jeans and flannel shirt. With those ones I did the demin with a flannel back and the shirt fabric with a peice of batting and the backing. I have done one in light weight demin with lace blocks. Demin comes in many weights and will mix and play well so long as your weights are compatable. Use a good thread and a shorter stich lenght.
Also a word about your demin, demins made with a strech fabric such as spandix don't work so well in a rag quilt project. It will fray but you will see little gray/black tubes of the man made fabric, spandix.