Depends on the Successor State and region. In Lyran, FedSuns, and FWL Core Worlds, poaching is looked as "Not our thing, dear," by polite society. In Outback/Periphery border regions, it's going to be a problem. Also, they type of game will matter.
Deer type animals would be frowned upon, but charismatic megafauna more likely. I expect there to be the occasional safari trip in the Inner Sphere. Here's an idea for a Time of War: the PC's are escorting an upper class politician-hunter, who likes to get his hands dirty cleaning things up. The PC's are mercs hired to keep him alive at any cost.