I've always understood the idea of "notching my tag" if I couldn't find an animal I wounded was more metaphorical than literal.... in that I could choose to stop hunting/trying to fill (or notch) my tag on a subsequent animal. I wouldn't actually "notch" my tag in a physical sense. I think another phrase I've heard used is "eating" my tag. Either way, the principle is the same... if I am reasonably certain I missed or just grazed an animal, I keep hunting... if I'm reasonably certain my shot was a mortal wound, I'll keep looking for it... but I won't be trying to kill another animal with the same tag. The question really comes when I'm not sure about whether my shot was mortal or not... then it's a tougher decision. This is one reason we do our best to record all our shots with the digiscope... especially when the kids are behind the rifle.
But, anecdotally... I've seen it go both ways. Once found a doe that had completely bled out from nothing more than a lower leg grazing bullet, just happened to get a good vein or something. I once shot a little buck that was hobbling around on 3 legs, the 4th leg was only attached by a piece of hide from the knee joint down... it was obvious that it had been that way for days... he was healthy otherwise, but I doubt he would have survived the winter on 3 legs... once shot an archery bull, and found a broadhead wedged in its vertebrae, completely healed over... looked like it had been there for years... once skinned a cow elk and found an inch diameter wooden stick/branch, 18 inches long, that had penetrated her hide and healed over. About half of it had gone between ribs and was up against the inside of her chest cavity, the other half was under the hide wedged up against the outside of the ribs! But she was healed and healthy otherwise. My son's 360 bull this year had a massive cyst or some sort of wierd gelatinous mass on its front shoulder... I suspected it was from a previous archery wound... but never found a broadhead... but the fluid sack was huge, like volleyball volume... must have been terribly uncomfortable.
Anyway... deer and elk are hardy animals... but at the same time, it doesn't take a lot to put them down, and I personally don't want to be responsible for the death of two animals if I only have one tag.