Let me be the voice of experience for you here! I used one fabric in a quilt for my daughter that seemed inclined to fray when I was working with it. Later on, every seam with that fabric in it frayed past the seam line in the quilt and was a big mess! I had to hand sew repairs all over the quilt where that fabric was.
Luckily it was a quilt for family and not one that was gifted out!!! I would definitely either use fray stop or some other type of treatment on the edges, or I would iron it to a backing of some sort. In some places that fabric frayed out over 3/8".
Now if I have fabric that seems to fray, either I don't use it, or I seal the edges. By the way, my fabric was also cotton, but not tightly woven enough.