If you wash the coutil you will wash out all the size, and the coutil will not be stiff and firm as it should be and it's the characteristics of firm coutil which make it such a pleasure to use for making corsets. If you want to make sure your coutil is pre-shrunk, then steam it.

What should you not prewash?

Cotton, linen, denim, rayon, silk and natural fibers should always be prewashed as they are likely to shrink. Synthetic fabrics, while they will not shrink, should still be prewashed to check for color bleeding. My rule is always to pre wash anything red.

Do I need to prewash stretch fabric?

Some of the shrinkage tends to ease as you wear a garment (like with jeans after washing) but lengthwise shrinkage not so much. So it's worth it to pre wash, if it's a garment that has a fitted style or if the fit and size really matters.