I can tell if a deer was shot during our early archery season versus later gun season. There are several people I know who can and we attribute it to the fact that during archery season(first season of the year) there is less adrenaline in the deer because it hasn't been running scared like they do during general gun season (last season of the year)
Something to consider is even if I killed a deer with my bow during gun season, it tastes the same as a gun shot deer. It is also tougher.