I think that is a stretch, both from a data backed perspective and a logical perspective. The data that I know of suggests that the mother has an outsized effect on genetic phenotype (expressed traits not just genotype) of its offspring. That is, depending on the in-utero condition of the mother, that fawn expresses traits differently. For males, it appears that the "decision" to push excess nutrition into body condition vs antler growth is made in-utero. Logically, it would make sense that a male that uses extra nutrition to increase body size has a higher chance of surviving weather events, droughts, potentially even predation. It is also not necessarily antler size that dictates success against other males during breeding, body size often wins there too, so lifelong fecundity I don't thing you can declare a clear winner between bigger antlers vs bigger body. All the data I know of suggests that fawn survival and future production depends on that fawns mother and her body condition during pregnancy.
I'm not saying that as an argument against the proposal, as you know I am behind it 100%. There are a number of benefits of this proposal from a hunting and hunt experience perspective and I think it is the better option when compared to the status quo of today and other options that remove significant opportunity (LE, etc).