I've used bamboo fabrics, which are basically like rayon. They do have a very nice drape. The fraying and wrinkling and tendency to shift while stitching would make these less than ideal for quilting, specially if it's a new pursuit for you.
However, if you have the time, and you feel like experimenting, why don't you make up a small project, and see how it works out for you? You may find that you really like it for some applications. Or you may come away convinced of the wisdom of using 100% cotton.
RST