It depends. If he is suffering or obviously having difficulty with living functions such as eating, drinking or moving fast enough to protect himself, then I would cull him. Otherwise, see what happens and give him a chance.
I had a hen who was attacked by our dogs. We managed to save her before they killed her, and she healed up just fine, although her thought processes seem a bit slow, even for a chicken. She still lays eggs and hangs out with the flock, but she'll be the first one a predator gets when I free range them if she's not around the others or the rooster. However, she deserves a chance, so she got one.