I think it depends a little. I have shot a bird and had his buddy stand over his dead body gobbling and strutting-after his initial surprise I called him back to shotgun range (could not shoot, I was alone-just wanted to see if I could) . How spooked was he? Did ya'll move after the shot? How hard did he bug out? Did he fly off or run off?
If he is the only game you have, give him a shot and see what happens. If you know of another bird and don't have competition for this one, I would give him a couple of days.