Lets keep in mind that a 2000 acre enclosure is only 1.5 miles across...that's not really enough for a "natural" movement pattern. Whitetails can move a long ways on and off an unfenced area. The fence would make it easier finding, patterning, and hunting game.
I don't think animals from fenced areas should be caounted in the books. Even if the hunt is difficult and the area is large, it's still an artificial enclosure.
I agree. You're still hunting an animal that you know is there. It's only a matter of time before you pattern him. There is no chance he could move out of the area or be killed by a hunter, car, or predator.