Yeah, I have wondered about the smell of cough drops, too. But I think a cough is certain to spook deer, while the smell of a cough drop might spook them. However, I try to breathe solely through my nose, hoping less odor will be emitted, but am probably just fooling myself. It has not actually been a problem as I have had many deer come in close with no reaction. One even walked up to my ladder and was smelling the rungs. (No, since it was still a baby, I did not try to shoot.) However, I have coughed in the presence of deer, and they turned themselves inside out scrambling away.
I don't wait for that first tickle. I put one in my mouth before I ever leave the truck. When it is used up, I replace a drop whether I feel a cough coming on or not.