I am sure you have had a lot of replies by now, but here is my two cents worth...
I would definitely wash both the black AND the white fabric, separately, of course. I would do this because of the difference in the shrinkage. Sewing preshrunk fabric with non-preshrunk fabric could cause a distortion in the quilt when it is washed. After all that work, you wouldn't want to take the chance that this could happen. In my world, I preshrink everything or nothing. That is the rule I stand by.