I think there’s likely to be a big difference in outcome between head shot and chest shot. Head shot, the gastrointestinal system remains sealed, and while it will keep the body warmer than is ideal, there shouldn’t be much (or any) movement of bacteria out into the surrounding meat. The membranes are waterproof, and until they start breaking down, should contain the microbes. So it probably all depends on how quickly it takes the membranes to deteriorate to the point that bacteria start leaking through.