Oh, for sure. On multiple occasions, even. The first that comes to mind is a man who assaulted Isabelle when she slipped away from Alec during one of their trips out when she was 14 or 15; Alec found him with her in an alleyway and stabbed him before even pulling him away from her. A few years later Isabelle had a flirtation with a stablehand that led Alec to believe they had had sex, so he tortured them both in front of each other before killing said stablehand. We could also count the American from the fic titled "Passion Play", who does not survive after what he tries to do.