if the intention is to ever wash the quilt again, then definitely yes, dry as well. in the washing, the softer silk loses it sheen and takes on a subtle brushed look and feel. it will not look like NEW silk anymore, even when crisped up. so why not dry as well?
i don't use polys because they don't behave like silk and most are heavier to start with, but if you are planning a wall quilt that will never be washed, you can use whatever you like and in the future have it dry-cleaned so there will be no bleeding. with no washing the ties, or any other silk, will keep all of their original color. mine will be used as a large lap quilt, and i expect to have to wash it from time to time.
an easy way to use all fabrics is crazy quilting with nice embroidery. same process for the silks. tell us what you decide to do. it would be interesting to get another take on this.