It might actually go a good deal faster. Firstly, humans make only a tiny fraction of all oxigen breathing species on this planet. I'd be surprised if we'd reach 1% of the total oxigen consume.
Secondly, if plant's can't do photosynthesis they'll die and rot. This rotting will again use up a lot of oxigen. The same will happen to herbivorous species and their predators. The whole planet would become a huge compost heap, so to speak. The oxigen used by bacteria in the rotting process and by simple oxidation of substances would very likely be a good deal higher than the oxigen all organisms require for breathing.
However, since the ecosystem is so complex, we have an equation with billions of variables. It's impossible to even make an educated guess.
The survivors of such a catastrophy would be certain bacteria and a lot of the archaea