Through grief and the resulting absence of motivation/interest in going on your health can/will be severely affected. Research suggests that unhappy people are more likely to fall ill, especially with infections, likely due to suppression of the immune system. It follows that illness leading to an earlier death than otherwise might occur seems distinctly possible. Additionally, a form of stress is at work and thus anyone inherently weak (heart, circulation, stroke) seems likely to live under very adverse conditions, and can therefore be brought to an early death.
Can you will yourself to die, all other things being equal - very unlikely I would have thought.