I hope to one day raise pidgeons for squab meat, and have done some research on the topic. However, I don't have any personal experience with them.
It IS possible to raise pigeons "free range" by setting up a dovecote, and this was the most popular way to do so for hundreds of years, if not thousands! In fact, I've heard that if you have a nice enough set up, your domesticated pigeons can bring home wild pigeons to roost in your dovecote, providing you with free meat if they stay and nest.
However, just as chickens and rabbits have changed from their wild cousins, domesticated pigeons have been selectively bred for many purposes. If you are looking for a squabbing pidgeon, they are referred to as Utility Pigeons. There are also racing pigeons, Fancy pigeons, show quality pigeons, and other types.
How you could control what they ate while free ranging would require require bird-prevention methods would be my guess, such as netting, fake owls, and pie pans on string.