A barred hen can only pass the barred gene down to her sons which proves Vick is a rooster (I don't know of any cases of a rooster becoming a hen and/or laying eggs)
I've never read where a hen with healthy' ovaries can grow testes and still lay eggs but they can certainly exhibit rooster behavior and crow like a rooster and mount the other hens. Their gender doesn't change regardless.
I had a wire dog crate in my coop flipped upside down with cardboard on the bottom to hold the pine shavings because its missing the tray that goes in it. Even with the door shut one of my pullets got inside by falling inside or squeezing to get in who knows!