You could do it. You could stabilize the fabric with nylon tricot fusible. JoAnn's sells it in small one-yard packages, so you could try it out, but for a quilt it is cheaper to order it by the yard online. I got some online from a drapery supply company and it was a lot cheaper per yard. The advantage of nylon tricot over other fusibles is that it stays soft (does add a lot of body; you wouldn't want to try to hand quilt this stuff!) and has a little stretch so it doesn't completely change the nature of the fabric. It is used a lot in t-shirt quilts.