Why Not?? ... I just finished a wall hanging this weekend of regular quilting cottons.
The binding is a tonal batik.
Similarly, there is no reason why you cannot mix quilting cottons and batiks in a quilt top too.
.........and yes, I am another committed pre-washer!
When I bring fabric home, it goes directly to the laundry room,
before it joins the stash or gets used in a project.