Man didn't "domesticate" chickens since there are no wild chickens.
Man did domesticate jungle fowl (genus Gallus) and later hybridized the jungle fowl to create what we know and call the chicken (Gallus gallus domesticus).
Now, outside of some gamefowl breeds most of the chickens we know today could not survive "naturally", not because of them being in coops and runs but because of the way they were bred. Man has bred most of the natural instincts out of the chicken because people want "pretty" chickens, ones that lay lots of eggs and or gives us lots of meat, in breeding for this man has sacrificed a lot of the natural instincts of the chicken and these birds are the ones that would die out completely if not for man.
Look at all the things we have bred into the modern chicken, Feathered shanks and feet, large combs, large body size, soft feathers, colorful feathers, tameness, the inability to hatch there own eggs, etc. these are the real reasons they wont survive naturally not because there in a coop and run.