They can be noisy as heck! But no, I doubt deer even flinch from the sounds of turkeys going about their business. I actually watched a flock of turkeys get into a fight one morning while I was on stand. They were beating the crap out of on another and out of no where, a big doe came out and actually walked toward the fighting birds, ears erect and staring intently at them. It was as if she was going in to break up the racket.
Something that I never realized this season was how loud grouse can be in the trees. I watched two of them fly back and forth from tree to tree eating and just making a heck of a lot of noise. Amazed me.