I have no problem hand quilting batiks when I use them in my quilt top. In fact, I love how they show the hand quilting stitches.
However, I volunteered to hand quilt a top for a friend. She pieced the backing, and used batiks in some spots. I used a cotton batting, and the parts where she has the batiks on the back are much harder to quilt.
I'd put a different backing on the quilt, and quilt away.