AT LEAST I've never had anybody kill a live mouse and then get bored with it and refuse to eat it, and after I've made a special trip out to Mesa to buy it, too. I have a friend who feeds about 50/50 frozen vs. live, and this happens to her all the time.
(I've actually noticed the babies are my best eaters. My 1 year-olds eat like clockwork, and then sit around hoping the big mamas won't eat so they can have third and fourth helpings. Doesn't help if I'm left with a rat that's bigger than they are, but they're handy little mouse garbage disposals.)