batiks and regular cottons are mixed all the time!
the only thing to keep in mind with batiks are---they are hand dyed- so there is almost always excess dye- they need to be pre-washed- the strips can be put into a mesh laundry bag so the don't tangle fray too much- or you can do them in a sink- but prewashing is really needed- especially if they are bright/deep colors.
as for wrinkling- all of our cottons wrinkle when the sizing is washed out- not an issue once they are a quilt-only when they are yet to be used fabric...after prewashing- they get ironed- then they are good to go- and batiks are wonderful to work with.