IME if it's a non lethal hit no matter how far you push them they won't bleed out. It may be possible but I've never seen it happen.

If you're unsure of where you hit the animal IMO it's best to back out. If you caught a liver the last thing you want to do is push the animal.

Bobco, I respect your opinion. You're not gonzo you';ve just got a diffrent perspective then I