Would a racing pigeon that refuses to fly home be better off being given to a bird rescue organization?

This pigeon in the southwestern United States.

What would be best for the pigeon? I've given him uncooked popcorn and white rice and an inch of water in a bowl. He seems calm.

http://imgur.com/a/ucyhP http://imgur.com/a/p9j45 http://imgur.com/a/eD62I