if you don't want to paper piece is why ask if you can?
you can use what ever you want for a foundation- it does not have to be muslin- muslin is (traditionally) used because of its inexpensive-ness, availability and the fact crazy quilts were not (traditionally) quilted but tied.
you can use what ever you want- you can battle with the blocks with no foundation of any kind if that's what you want to do-
a stablizer of some sort really helps with the different fabrics/textures