As others have said, a camo gun is certainly not necessary for hunting turkeys. movement is the big thing. When in doubt, keep still. As you get experience out in the woods with turkeys at close quarters you will learn when and what types of movements the birds will let you get away with. I'm still shocked some times by the weird contortions a turkey in shotgun range will let me do without spooking. But, as a beginner, the most important thing you can do is keep still, and when you do need to shift, keep the movement slow and smooth. Fast, jerky movements signal danger to a turkey and they will skedaddle and ask questions later (Trying to quick-draw a turkey just about always ends badly in my experience). A slow deliberate movement is no-where near as alarming to them, and in some cases may even pique their interest.
Having said that I have a camo gun, and the biggest benefit I see from it is the additional weatherproofing it adds to the gun. Getting rained and snowed on is no big deal whereas my old black 870 would start to rust if it even looked like rain outside.