Yep. If yeast are provided with oxygen, they can convert an equal amount of sugar into *four times* more CO2 (if I recall right), producing no alcohol.
The problem is that air is mostly nitrogen. All that inert nitrogen, which is insoluble in water, has to be purged out of the system. Which, depending on your diffusion scheme, creates bubbles that carry away much of your bonus CO2 uselessly to the top of the tank. Or fill a reactor until it burps out nitrogen and CO2.