With endangered or valuable birds, the bones can be pinned. I doubt whether the RSPCA will fork out that much dosh for a common pigeon though.
It all depend where the break is, but often the bone will not heal, or knit at an funny angle, making flying impossible.
I did have one of my pigeon hit a wire and break the 'elbow' joint. These injuries are notorious for not mending satisfactory. This one however seem to have grown a calcified 'knobble' over the joint and could eventually fly slowly at a funny angle. This bird lived for a long time.