I would think you need to finish the edges in some way-
all of the tied quilts our sewing group makes have bindings. The backing material would probably be fine, if you like it showing on the front of the quilt.
I made one denim quilt where is stitched 3 lines of stitches ( close together- 3/4” in from the edges- then clipped every 1/4” up to the stitching lines giving it a frayed- chenille like edge.