I did not prewash duck cloth (canvas) for the big ironing board my dh made for me out of plywood. However, mine is a natural muslin color. It is stapled on; I will simply cover with another layer of duck if/when this layer wears out.
For your yellow cloth, I like the idea of using a portion of it to iron some white cloth with steam. I'd probably use a white cloth that has been washed, so that there are no finishes that might get in the way of color transfer (a dish cloth would probably be fine). If color doesn't transfer with the hot steam iron, then I would also leave a piece of the yellow duck in a glass of water overnight to see if any color bleeds into the water. Afterwards I would also rub the damp piece of yellow duck against several white fabrics to see if there is any color transfer that way.
If there is no color transfer, the only reason to prewash the duck is if you are making a removable cover that you plan to wash later on. In that case, you must prewash to get the shrinkage out of the way before you cut and sew.