I would expect that some people would be able to drink more blood than others without vomiting. Some people might not vomit at all. There's nothing really physiologically wrong with blood as a food -- the thought of it is repulsive to many people, though.
In Africa certain tribes drink blood straight from the jugular of live cows. It's much more economical than killing a cow every time you want a meal. This way a single cow can serve as a consistent source of protein for the entirety of its life.
You'd vomit after drinking "enough" blood due to iron poisoning. How much is enough? Well, that depends. How much alcohol do you have to drink to get as drunk as your friend? It all depends on how well your body handles it.