You can test with a small scrap of each fabric. Drop both in water, let soak for awhile, then smooth then out on top of each other on a paper towel to dry. If there is no dye in the water and if no dye transfers to the white, you do not need to prewash.
If there is some slight dye bleed, you can still skip prewashing if you plan to do the first wash of the quilt with Synthrapol in either a domestic top loader or large laundromat front loader. Synthrapol works best with hot water and lots of it; domestic front loaders often do not use enough water for this.