Barnes, I'm confused with your post. And I'd like to converse a bit more.
I would get on it with a rifle, but not a bow.
Why? Do deer bleed better with bullet?
If he’s able to run, you’ll chase all over the country side before he expires or lets you within bow range.
So what?
I would let him bed down and hopefully bleed out.
You'd rather hope then go after him? You already stated that:
Deer beding and resting up = coagulation = less blood loss.
This is very true.
However, if the wound is minor enough that resting will prevent the deer from bleeding out
Have you actually ever seen the capibilities of a wild animals ability to form blood coagulations? It is nothing like a human. I work with a tracking dog and as such have to keep a fresh inventory of blood for training purposes. The capilitiy is amazing, I can gather up two quarts of fresh blood and will not make it back to the house within an hour and the entire batch is totally coagulated (I have to break it down with a blender when I get back home). What I am saying is that you would be surpised what type of wound can coagulate. It doesn't have to be minor.