I'm a pre-washer and have been doing a 'scientific' study. I've been measuring the fabric before and after laundering and have found that almost all my non-batik fabric has been shrinking about 2" across the width of fabric, and almost nothing across the length. Don't know how you feel about shrinkage, but you may want to wash the most color saturated piece. This way you can check for bleeding and if you measure before and after, find out if it shrinks.
I'm going to continue to pre-wash. I use cotton batting and like a bit of a crinkly look, but am worried about the fabric shrinking unevenly.