It's not supposed to emulate actual blood on your eye.
It's supposed to be a little shocker, like when you hear a gunshot and all you see is a splat of blood squirting at the window in the setup of a PG-13 crime show. What it's supposed to emulate is the disgust you would have for such blood effects, but the only way to really get this across to the player is by having it squirt directly on his screen.
Same with the dirt that hit your screen in Brothers in Arms when you were behind cover and someone shot at you. Obviously you don't see specs of dirt on your vision in real-life when that happens, but your vision does get obscured and you have a feeling when dirt and debris hits your face. Disgust, shock, pain... The stupid looking dirt effect is just about the most realistic way to get this across to a player. If anything it wasn't extreme enough in BiA.
Personally, I'd say yes to both the blood as described by the OP (but also for other situations, like stabbing someone with a bayonet or shooting someone from very close range) as well as to dirt and whatnot when a shot hits something close to you to increase the effect of suppression.
None of this applies to the weird visible eye-veins screen thingy that's employed by Call of Duty when your health is low. That's just strange. It gets the point across, I guess, but it's basically nothing else than the Gears of War logo fading in when you get hurt, like in, well, Gears of War. Except Gears of War is more honest about it by making it an abstract logo and not a pseudo-realistic eye-vein thing.
