I think it would turn out very similar to a rag quilt, and a charming one at that. I'd probably shorten my stitch length and be fairly generous with the seam allowance.
There's a woman named Kellie Wulfson in Australia, she used to have a wonderful blog called "Don't Look Now" but I think she shut it down when she opened a quilt shop. Anyway. She made the most beautiful applique quilts and they were all raw-edge straight-stitch applique. She used a shorter stitch length and went around each piece twice. These were quilts made for her 4 children, so they were used and washed.