I can't comment on how much destruction eagles can have on a turkey population, but I can testify to the fact that they will chase them and it appears try to catch them. 2 or 3 years ago I was working a mid day gobbler on a power line when a big bald eagle swooped down and tried to grab him. The gobbler kinda ducked and ran then flew into the nearby creek bottom. Looked like the gobbler flew up into a tree and the eagle flew back up real high and then dove back down towards the creek bottom. I then heard big heavy wing beats of 2 birds and it sounded like the chase continued on through the bottom. I never saw anymore of that gobbler (that I know of) but 10 minutes or so later I caught a glimpse of the eagle flying back up real high over the power line. I then watched him and he lit in a big ol pine just off the line. Seemed like a perfect spot for one to hunt and watch for prey from a long distance. Not sure if that gobbler was just a random attempt at a meal or that eagle routinely chased turkeys there. But, I have found a couple big piles of turkey feathers along the middle of that power line since then where it's obvious something had a turkey happy meal.