You could probably wash the pieces by putting them into a mesh bag or pillow case but I have found that different fabrics shrink and fade differently. You could end up with pieces that won't fit together anymore. I know some people don't prewash but I have learned the hard way to prewash and I have read of others who have had bad experiences too. You may get by 90% of the time but those other times could ruin expensive fabric and a lot of time. I guess if I were in your shoes I would go ahead and make the quilt top and then wash it before I quilted it.
Lynda