They're not just drama queens (I don't doubt that there are some who exaggerate to get that little extra rest). You see it in the cases when the referee doesn't stop that they are handicapped for a while.
I actually know that a groin shot which didn't properly land may start to hurt only after the adrenaline goes down after a situation on the street. And a good friend's acquaintance told that he thought only to have been punched in the torso when he woke up from coma after having got stabbed. Another one I know of just felt it getting warm around the area of his kidneys (due to his blood), before passing out.
BUT groin shots and knife stabs are a different thing than eye pokes. With the eye it's not necessarily so much about pain, it's more about uncontrollable reaction. You just can't control the tears to start to run and thereby obscuring your vision and you barely can't control your eyes from squinting, because that's just an automatic reaction.
Fair enough. I often overreact on this topic because I've heard so many people tell me that they could beat Fedor with an eye-gouge or groin shot...