I don't think that I would wash a pieced quilt top. I suspect it would fray and become very unstable.
If you want to wash the pieces before you piece the quilt, I do have a hint. Gently wash the pieces (I use quite warm water) in the sink, then put them in your salad spinner a few at a time and spin the water out. I then usually press them dry.
Yes, I did say the salad spinner. I read in on another post, tried it, and it works great.