I think washing before cutting is worth the effort. That said, I do have a large stack of fabric that is unwashed and taunting me.
It is a bit of a bother - but I think trying to remove dye that has bled and trying to repair seams that have pulled out because of shrinkage is a bigger bother.
From my experience, a small piece of fabric (a scrap or a precut) can bleed just as much as the larger piece of fabric it was cut from.