The only way you can release them and expect them to come back - is if they were born and raised in your yard. Or, they have a mate that they know is in the coop in your yard. When I was 12-15 I had a pigeon coop and raised some. They are not very interactive or much fun. One day the escaped - they stayed around the house and neighborhood but never went back inside the coop no matter how much food or water I left out. Funny thing - ten years later I was in the military and home on leave.... and the birds were still hanging around our house!
Today I have a blue quaker, two sun conures and two green check conures. The quaker parrot by far is 2,000 more fun than a pigeon. Quakers - are in the top ten list of birds that can talk. Mine loves me, eats breakfast, lunch and dinner with me - says about 40 things - hates my wife....... but he is a real pal and lots of fun. My wife - she cant go next to it..... me, I can pick it up by the tail feathers or flip it upside down on it's back and he doesn't care. I put him on the floor - he runs in little circles yelling,, 'weeeehooo weeehooo I'm a squeaky toy!!'. You wont get a pigeon to do that.
I had a pair of pigeons as a child. I kept them in kind of an indoor/outdoor nesting box wired to the tv antennae outdoors. We'd take them to other towns with us, one at a time, and release them so we could see how long it took them to get home. We did leave the cage open except when the lawn boy came because they would attack him. They were just regular barn pigeons like you see everywhere. Sarge and Pandora.
I am looking into owning a pigeon and was wondering what breed is best? I was hoping to keep it outside, and is it possible to let them out during the day so they can fly about at their own will?