Well, it's true that if you leave chicken feed out where mice can get to it, it's possible that some may show up to eat the feed, just as they would if you left any sort of feed out (such as dog food or cat food or wild bird seed). And it's also true that you don't want a mouse or other rodents pooping in your chicken feed.
But will they bother the chickens? Uh, not likely. Observe:
Chickens are omnivores. If you think about it, you know they eat insects. But what you might not realize is that they'll eat little animals such as mice, moles, shrews, small snakes, voles, frogs, newts and so on, too... if they can be caught! And as you can see, chickens can be pretty efficient predators. They're often better mousers than actual mousers.
So, do keep your food secured. You don't want your chickens eating poopy feed, and you don't want to be waste your money on feeding the local rodent population. (You can see tips below in the related questions.) But please don't worry that your chickens will be actually scared of them. No... chickens think mice are tasty!