I'd likely not do it unless there was an actual reason to do so. I'm a tenacious sonuvabich, I'd try to beat the odds till the very end. If there was a reason to commit suicide, that would be another matter. And by reason, I mean that there would be actual benefits to my death, while my death is assured anyway.
Say, all my friends are incapacitated, but we're otherwise safe in hiding. However, I've been bitten by a zombie and if I don't kill myself I'll turn and attack my friends before they can recover. But I also can't just leave before I turn since that would give away our position. In such a scenario, where I'm dead anyway and my continued existence would have a negative impact, I'd consider slitting my wrists or some such for the greater good.
Say, all my friends are incapacitated, but we're otherwise safe in hiding. However, I've been bitten by a zombie and if I don't kill myself I'll turn and attack my friends before they can recover. But I also can't just leave before I turn since that would give away our position. In such a scenario, where I'm dead anyway and my continued existence would have a negative impact, I'd consider slitting my wrists or some such for the greater good.