I doubt it would have that much effect on small game populations. It would be interesting to see what would happen if all seasons and bag limits were removed on all small game species. Give me a chance to vote on it and I'd vote for trying it for a few years to see. Of course, it will never happen.
In many places in AL, it wouldn't make much difference with deer and turkey either. Places controlled by large landowners and large clubs would probably manage things as well, if not better, than the state. Where it would be really detrimental to the populations would be in the areas made up of small landowners. I suspect you'd see both deer and turkeys virtually wiped out from some places. I couldn't vote for that.