well here in NH turkeys don't seem to bother the deer they seem to feed side by side I actually see it a lot & I am begining to think the deer like to be around the Turkey's as they are a very alert animal
I spoke just last month with a guide from Maine about this very subject. It's his opinion that large flocks of turkeys, now roaming the Maine woods are causing some "feed" problems with the deer population. He described it as such: A deer will munch a few fallen acorns and mozy off. A flock of turkeys will stop under that same tree and eat every single acorn on the ground. Of course, feeding in fields it a bit different as the turkeys are eating seeds & bugs and the deer grasses & leaves mostly.I would say Yes from what I've seen, I do believe Turkey push deer around by consuming so much of the available food sources making it difficult for deer to browse comfortably.
A couple years ago I asked a biologist about this very subject and he agreed.