I'm too tired to look into the math right now, but atmospherically I would say that carbon dioxide accumulation would be quicker and more harmful than actual oxygen depletion.
But I agree that lack of food would be quicker than both.
(On the other hand, there are bacteria that don't need photosynthesis to survive. So it will not mean a total extinction of life. With time, more complex forms could evolve, resulting in a completely different evolutionary tree.)