Hi Flipper - I have tons of cat stories having had many many cats over the years. And yes - some of them have tried this but I have no patience with such so they soon learned to skip that procedure with me. I suspect it is one of the few times they catch us sitting down for any length of time.
But I also had the cat's litter box in the bathroom and it got so my last cat, Fluffy - a big old longhaired orange tom - generic looking cat with the white nose, would come and use his litter box while I was using mine. Kind of a routine - if I thought it was time to do the bathroom thing he thought so too. And he covered while I flushed - totally synchronized. Now that's togetherness. LOL.
Another cat I called Peter - a Snowshoe Siamese and a real character - brought a mouse in the house to play with. Then when he tired of his play thing he deposited him in the bathtub as the creature's playpen and yes the mouse was still very much alive. When I came in the bathroom I was sure of how the creature had gotten there but not sure of which cat was guilty - the poor little mouse was totally unable to escape the steep shiny walls. Well I can't bear killing little creatures nor watching the cats torment them so I got myself a paper bag to catch him and deposit him back outside. When I had successfully finished the task Peter showed up and showed his disappointment at my lack of appreciation - there was no missing the fact the mouse had been his personal trophy and he also let me know what he thought of my unjust robbery as only a Siamese can talk in that nasal twang.
Then another cat I had called Cubber Cubs - brother of Fluffy - they both came to me when tiny kittens - their mother brought them up the hill into my yard and moved them in with my other cats - her brother was Peter - came into the bathroom just as the water was emptying out the drain from my bath. He jumped up on the edge and I thought to myself he is very likely to slip right into the water and not like it but before I could do anything about it - he had jumped right in - the water was only about 2 inches deep but it came up to his bellyand instead of being afraid he just plodded right down to the drain to watch what was going on. I guess he was fascinated with the gurgling sound and wondered what sort of creature purred like that. He was so funny as he kept twisting his head round and round with the water swirling trying to see down into the drain. And ever after he was easy to give a bath - he had very little fear of the water and would just stand there patiently while I sudsed him up and rinsed him off. Amazing cat and he looked just identical to St. George's orange tabby above.