If I am not mistaken, your question is what will happen if oxygen production ceased completely. As oxygen is a highly reactive gas, obviously it would be depleted eventually, as you predicted.
The Earth's atmosphere currently contains about 21% Oxygen. This is about $10^{18}$ or a quintillion kilograms. Since 1 atm is 101 kPa, the partial pressure of oxygen at sea level is about 21 kPa. Modern day humans are unlikely to survive when the partial pressure falls below 8 kPa
Oxygen can be consumed by many different methods. One is to bind oxygen to biomass in order to produce $\text{CO}_2$, water and energy. With no plants to reduce the $\text{CO}_2$ back to biomass, there is not only an oxygen problem, but a food problem. If plants continue to reduce $\text{CO}_2$ but do not release the oxygen, they would have to keep the oxygen in oxidising agents, separate from their energy stores, which would presumably trigger, in the long term, animals that can process this.
In any case, with no recycling, the oxygen is consumed by biotic processes at the same rate biomass is oxidized, I'll assume that the production of 100 billion tonnes C/yr, according to wikipedia, also ceases, because I don't think plants can keep large amount of oxygen in them, so they die of the free radicals eroding their DNA. 279
There are only 560 billion tonnes of biomass apart from bacteria though, so they'd only sequester around 1.5 trillion tonnes (1.5 quadrillion kilograms) of the 1000 quadrillion kilograms of Oxygen. Just 0.1%, not much.
Where did all the rest of the carbon go? Well, some of it is in bacteria, but a lot of it is in the stuff we're currently digging up and burning. If all the plants die, it'll take a while for people to realize that burning all those fossil fuels isn't such a good idea, but it will happen. We'd likely switch to carbon free fuels like Uranium and Plutonium (in fission) or, eventually, hydrogen and helium isotopes for fusion. The problem of feeding ourselves is the immediate one. Happily though, humanity has stored some seeds in seed banks. They won't be modified. We plant those and the ecosystem will eventually find itself on its way back to normal. Might take a while though. 279