I think it's fine, but that's a personal opinion that I know some people don't agree with.
The chickens themselves don't seem to care, once it's dead and not flapping around.
They might not eat the insides thoroughly enough, so you'd have to pick some up and dispose of it at the end (you don't want it laying around to attract predators.)
Some people do not feed chicken to chickens, because they worry about spreading diseases. If the chickens all come from your own flock, I don't think disease is much of a risk-- they've already been exposed to each other.
But I would not want to bring in a live chicken from someone else's flock, butcher it, and feed the insides to my own flock. (I would worry about importing diseases with the new bird.)