Maybe you can add Call of Duty style of bloody screen effect instead of a health bar? It would get worse with damage and go away smoothly when you don't get any damage for a while.
I would do it with alpha so on the edges it would be opaque and getting transparent to the center. And of course some kind of blood texture, not just a simple gradient.
Yeah I do like the idea, I think it looks quite natural on CoD4 and stuff, you don't have to check your health but you always know how much health you have.
