Beautiful quilt!
I've backed batik quilts with batik backing and had no trouble quilting it. (I quilt on a DSM) So if batik is how you want to go, I say go for it.
BUT...that top is glorious so you don't want to detract from it; and a king-size quilt worth of batiks for a backing isn't going to be cheap, even if you buy wide backing. If this were MY quilt, I'd go for a simple, solid-color backing that coordinates with the top, and use batik for the binding.
You kinda can't go wrong at this point, though.
Very nice quilt.