Would the strain of chemotherapy hasten her death? I don't know. Would it extend her life? I doubt it.
What confuses me is how chemo can improve quality of life. From everything I have heard the treatment is distressing, to put it mildly. Since your mother's disease is terminal, I should think it would be kinder to let nature take its course. Of course, in that case, a whole bunch of people wouldn't make as much money.