There is absolutely no way to know this. Speak with palliative care specialists; ask for hospice. Sometimes, if a person is eating, drinking, getting supplemental IV fluids or tube feedings, these things can go on a long time. They almost always do treat pneumonia, and even without treatment, pneumonia, once known as "the old person's friend" doesn't always kill. Please be quided in your individual case by the hospice personnel,and I am so very sorry for all you are going through.
Well, according to Dr Google, death from untreated gangrene can occur in as little as 48 hours:
What happens when gangrene goes untreated? Gangrene can spread through your body and cause you to go into shock if left untreated. Shock is a condition marked by a variety of symptoms including low blood pressure. Shock can be life-threatening and is considered a medical emergency. Gangrene is a medical emergency that could lead to amputations or death.
If your loved one refuses treatment, now is a good time to call hospice.
Who is legally able to advocate for your friend? Is he on anyone's radar (besides yours)? I'm not sure anyone can know how much time he has left without knowing other medical facts of his case.
What happens when gangrene goes untreated?
Gangrene can spread through your body and cause you to go into shock if left untreated. Shock is a condition marked by a variety of symptoms including low blood pressure. Shock can be life-threatening and is considered a medical emergency. Gangrene is a medical emergency that could lead to amputations or death.
If your loved one refuses treatment, now is a good time to call hospice.
Wishing you the best of luck moving forward.