Of course they can. Its rather difficult to kill one but by no means impossible. In the case of Godou, even an ordinary person could kill him if they had knowledge about his abilities and limitations. Nobody could take them in a fair fight though.
EDIT: To elaborate, Campione have a wild instinct to avoid traps, and they are crazy durable. Oh, and they have enough magic resistance that all but the strongest spells won't even scratch them. That's not even counting their powers. Short of a bomb going off under them or a sniper getting them in the heart they probably won't die. Still possible, but not all that likely. Unless your Salvatore, who's power is being invincible...