In theory, one can use any fabric for a quilt just like our ancestors did. Rayon, although it takes on dyes beautifully, is also known for not being able to hold color (note that the labels on your mother's blouses will probably say "dry clean only") and it is also known to shrink if put in hot water. If you're aware of these limitations and allow for them, I think you'll have a wonderful memory quilt.

I second the idea of reinforcing your seams. I've made a few blouses/tanks/shells out of rayon and found it best to either serge and topstitch the seams, or do french seams and top stitch.

I inherited a bunch of perfectly square rayon pieces (about 7"). I've made several personal sized quilts out of it, an am working on a beige/lilac/black turning twenty type design now, using additional WOF lilac strips

Just don't hit with a really hot iron