I would guess that nutrition plays a role but it is not the only factor. When you think about the primary purpose of antlers (sexual adornment), they are really saying that I am fit and healthy enough to expend this much energy on growing antlers. The formula is basically trying to maximize the amount of genetic material passed on to future generations. When a buck is young, it is spending a lot of energy growing and has less to put into antler development. Once growth is done and it only has to maintain body size, it can afford to put more energy into antlers. In those earlier years, the thinking goes that if it can produce larger antlers sooner, it will have more opportunity to pass on genetic material. That presumes that doe availability is a limiting factor. The longer a buck lives, the more opportunity for injury and disease to set in. These are energy drains. At some point the evolutionary strategy changes from having more sex now before I'm shot or hit by a car, to having less sex now and living longer so I can have more over my life time. (These are obviously not conscious thoughts but an underlying evolutionary strategy). During these later years, less energy goes into antler development and we say a buck is on the decline.
I'm sure nutrition plays a role, but it may or may not be the limiting factor. Other factors like disease prevalence, sex ratios, and overall deer numbers are also likely factors. There are probably other factors involved like the personality of individual deer. Some buck may stay more local and succeed through dominance while others may range further and succeed by being more sneaky.
While I believe we can say with some confidence that nutrition can play a role at what age buck antler size begins to decline, I don't think we can necessarily extrapolate to saying with confidence that feeding protein pellets in the spring will change this age.
Thanks,
Jack