I don't prewash, but do test fabrics I think might run before using them in a quilt.
I always wash the quilt in Synthrapol for that first washing (suspends dye particles in the water so they don't settle into other fabrics) and also use color catchers if there are any suspicious fabrics in the quilt.
The only time this might not work is if you have a truly bad "bleeder" fabric -- the kind that bleeds a *lot*, not just a little, and keeps on bleeding forever. You can spot this kind of fabric by placing a 1" or 2" scrap in a glass of water; it will leave ribbons of dye in the water. With yardage, I would wash a fabric like this in Retayne to set dye and then re-test; with your pre-cut pieces, I would just not use that fabric in the quilt.