I've done this several times...most recently in a baby quilt that had pre-washed fabric for the outer border and backing and un-washed jelly roll strips for the inner border and binding. Came out great...lots of crinkles and very soft.
But I do always use the Color Catcher things...and if the quilt is a gift and has colors I'm afraid will bleed, I give a box of the Color Catchers also along with printed washing instructions.