L.M.
I don't know about Corelle, but my mom put my Cabbage Patch Kid in the washer when I was a kid and she turned out very good. I don't know why you would wrap it in a pillow case though... don't you want the soap and water to get to it to get the smell out??
Obviously, if it is a doll with any electronics you can not wash it in the washer....
I'd give the company a call. I know the American Girl line allows you to send the doll to the "spa" to get cleaned or hair fixed.