I'm not sure I buy the oyster shell thing. I haven't seen any data. For deer, there are no studies that show mineral supplements have any positive impact on the health or antler development of free ranging herds. The reason is their highly varied diet. Different kinds of plants have different abilities for mining minerals. There are very few places in the country where soils are so depleted of minerals that, given their highly varied diet, minerals would be a limiting factor on a free ranging deer herd. There are also risks using point source attractants like mineral blocks and licks. Some diseases are more easily spread with the increased face to face contact point source attractants encourage. The best way to apply minerals for deer is to broadcast them on your food plots (N, P, and K along with micros) as call for in your soil tests. While deer do get the minerals through eating the plants you grow in your plots, more importantly, they get the high quality foods they help you grow!
As for turkey, I haven't seen any studies at all. My hunch would be that, since their diet is even more varied than deer, supplemental minerals would not benefit them much either, but that is just my hunch.
I would contend that the biggest factor in turkey populations in my area (zone 7a) is spring weather. Winter kill may be more of a factor further north. In my state, the regulations have limited the largest hen predator in the fall, opportunistic deer hunters. Next to spring weather favoring disease that kills young poults, poult and nest predators would be the next limiting factor. The first thing we can do about that is habitat improvement. By working on the arrangement between nesting cover and brooding cover, we manipulate the vegetation to favor prey over predator. We can control some predators, but not others. Avian predators are often protected. Coyotes are an interesting predator when it comes to turkey. They are clearly a negative for deer, but it is not that clear for turkey. While they do predate nests, poults and even adult hens on occasion, they also predate other turkey predators, especially nest predators. Some studies show that after coyotes establish in an area, it has a slightly positive impact on turkey populations. By reducing skunk, opossum, fox, and other predators, they remove more risk to eggs and young poults than they take.
Thanks,
Jack