Yes, wash the dirty feathers a.s.a.p. but I have to tell you- I've had a lot of dirty butts through here but we had our first truly pasty chick last week. The vent itself kept sealing shut, like it was pooping super glue or something! Eek.
I've found that the easiest way to clean crusty butts is children's bubble-bath/soak. It doesn't require rinsing, and you don't have to immerse the whole chicken.
Prepare a small wash tub with warm water and half cap-full of bath liquid. Have some terry hand towels handy. With the chicken under your left arm, back her up to the basin. Splash warm, sudsy water onto the crust until it softens and loosens, then gently pull it off the feathers. This generally takes no more than a few minutes, then towel or blow dry.
I do crusty feet the same way. With the chicken's head cradled under your arm, they usually feel calm, and backing them up to the wash basin is a natural position for them.