Well, my horses eat a lot of carrots and they seem to fart just as much as horses that won't touch carrots. So who knows, but I kind of doubt a few carrots does anything either way for something as big as a horse.
Mine doesn't fart much and she gets lots of carrots. However, previous horses all got lots of carrots and farted all the time. Maybe Triple Crown Senior keeps them from farting! My unscientific research points to YES.
I don't see how carrots would do anything. Also, I don't think that carrots in those human foods would have any effect. If they are in something that is going to be cooked, any "beneficial" enzymes would be getting inactivated by cooking temperatures before they were eaten, anyway.