No, they don't, if you train them.
I have a set of weak spring mouse traps that I line the edge of counters with when I adopt a new cat.
Sure there are a few wakeups in the middle of the night, but they DON'T want to go there.
/johnny
I love cats and my husband didn’t....our first cat had go go when it decided our dining room table full of food and we were eating, belonged to him and he landed in the middle of the table beside the mashed potatoes....the second one a year later use to just stare at hubby, freaked hubby out, I think cats know when you don’t like them and they try to quietly drive you nuts.....sometimes kitty would sit on the 1/2 wall between kitchen and family room and stare at hubby with his tail twitching back and forth...especially when hubby was trying to nap on the couch under the 1/2 wall...Kitty has to go and no more kittys. Always had a dog tho.....