There are a couple very valid points in this thread:
1) Something like this would have to be built into the system as a whole and become one of the factors of balancing. As an add-on to combat, it would introduce an odd dynamic to the combat cycle and likely producing a very non-linear behavior to damage dealt over time and the rate of health loss for a PC or creature.
2) The way that a body reacts to physical stress, injury and life-threatening situations is indeed known to sustain a person, often overriding the flight-or-fight instinct and potentially even making a person fight more aggressively and effectively.
The whole concept of HPs itself is a sort of balancing factor between realism and fun. Remember the last part, as games are supposed to be fun.
As I said above, one's stamina will come into play in combat situations (and likely others as well), and this will indeed impact how effective one is during combat in some way. It will affect some more than others, of course. It all depends on how the character is built.