It is possible to drink blood from zombies but not zombie villagers, husks or drowed.
Biting could be an attack disregarding whether if it's something that you can get blood from or not. As undead you won't be picky about what you have in your mouth and how it tastes anyways... especially if it can be beneficial in other ways- raising your offensive capabilities! Also could be useful if there was a way to rebind it.
Raw meat can be eaten(munched/sipped?) to get some blood or processed for greater amounts of red liquid. Could be integrated with Anthropophagy and Chest Cavity.
Integration with Nutrition to gain nutrients from blood? Probably should depend on type of mob and quality of blood.