I probably wouldn't try to use the scarves in a quilt. I think your idea of using the colors is great!
If you want to try using the scarves, I'd recommend using fusible tricot on the back of a small piece and then wash it to see if it is going to work -- colors don't run, doesn't shrink weirdly, fabric hand seems soft enough. Fusible tricot is available in a small packet at JoAnn's, or online in large amounts from drapery supply stores. You could also try other lightweight fusibles if you want to make several test swatches. I just doubt it is going to be worth the time and anxiety to do this.