Er, no. The majority of the time it would indeed run off, andA: Come back the next day with nothing (arriving unerringly at feeding time)B: Come back the next day with a small http://garfield.nfshost.com/1981/07/05/C: Come back the next day with an object other than what you wantedSecond most often, we'd have the "look at you like you were an idiot" response, then "on that odd occasion, they would do what you say. It would be as rare as winning the lottery..." and we're talking you'd get that repsonse maybe once in 20 or 30 full playthroughs. The "Do all quests and achievements in one playthrough then back to CoD" crowd would regard having one's cat do as asked to be a myth, as would roughly half (or more) of the playerbase anyway.
(About cats being picky eaters) "This is no gourmet; look where he licks. What gourmet licks his own butt? That's what makes you mad! They won't eat the food you've got for 'em, but then he goes over there and licks his butt. They ought to make butt-flavored cat food."