Fun read on the topic, Double L. I will say, no matter how we choose to supply food and habitat in any amounts, wild populations will tend to still follow a sigmoid/S curve in population densities. As the food and environment allows, there can be exponential growth to a point a carrying capacity is reached. But then limiting factors such as weather, predation, disease, and resources will tend to cause a drop in the numbers until those factors once again favor repopulation to or above carrying capacities. This is true with plants, prey, or predators all to some extent. So no matter what we do, there will be these fluctuations tho our efforts may help to minimize the peaks and valleys of the curve.
So in reality, we truly have limited control regardless of our thinking , at least in my opinion. The caveat with the whitetail, is that they are one of the few animals than can supercede carrying capacity and maintain it for quite a while before nature takes charge and brings it under control by starvation, disease, predation, etc. A oversimplified formula you may use is N/T=B-D. N=change in number, T change in time, B birth, D death. Of course using some type of educated guess on survival and births. The questions you ask of yourself are the same we all wrestle with if we are trying to manage habitat. Thanks for the discussion.