So I actually HAVE accidentally cut one of my cats claws at the quick. Funny enough, I don't think she even noticed, she was more annoyed that I was holding something to her paw (to stop the bleeding) and hadn't let her go yet than, you know, the fact that she was bleeding. She didn't even make a noise when I cut wrong.
None of our cats have enjoyed getting a nail trim, despite our best efforts. So, we have to resort to bribery with cat treats to keep them calm lol Otherwise they WILL fight me tooth and nail, literally, to avoid a trim.