That's ****ing disgusting. No, it doesn't all go down, there's a bend in the pipe stopping all the smells from coming up. If you pee in the shower, some of your pee will stay in there. Also, bathtubs don't generally flush things down completely, but you're practically standing in your own pee for the duration of the showering.
If my housemate started peeing in the shower I'd go pee in their bed.