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Probably the opposite. I'm sure someone has told you an arrow kills by causing massive blood loss, not shock. A deer shot through both lungs is going down quite quickly. How far he travels depends on a lot of things. I've shot 80 something deer with a bow. I've had them go a long ways and no ways at all. The ones where I hit heavy bone or heavy muscle seem on average to flee quicker, further and under more panic. If on the other hand you slip an arrow between the ribs and catch nothing butt soft tissue, they sometimes just take a hop or two and settle right back down. They react to the noise. They don't feel the arrow like they do when you're busting bones. I've had them just walk a couple steps and fall over this way. The deer shot through the shoulder will die in about the same time... it's just that fright makes him travel further. I personnally think it's much better to watch one flop over within sight.