I don't think that's quite right.

Rayon / viscose is basically: you take some cellulosic material (wood pulp, could be bamboo pulp, whatever) and dissolve it in a strong basic solution. You now have cellulose in solution. Then, you shoot it out of tiny holes to make almost 100% cellulose fibers of whatever diameter (the hole size). Then you make this into yarns and weave it into something. You can make it seem like silk, cotton, wool, whatever.

I don't think the feedstock has much to do with it (though lignin-containing vs. not is an issue).