I agree with jay.. By mass yeast can produce just under 50% fermentable sugar mass in ethanol.. A 2kg(4.4lbs) bag of sugar will yield just over 2lbs of ethanol.. Now a mole of ethanol weighs roughly 0.1lbs, so you're looking at roughly 20 moles of alcohol..
Now the fermentation process for glucose is:
C6H12O6(sugar) -> 2C2H5OH(ethanol) + 2CO2 + heat
So you're getting 1 mole of CO2 (thats 602000000000000000000000 molecules btw) for every 46mL of 'pure' alcohol produced, which works out to about 3 beers..
Now 1mole of an ideal gas will fill about 5USGallons at standard temp/pressure, so that 4lb bag will create enough over its entire fermentation period (which can be 3-30 days depending on lots of stuff) to fill 100Gallons or about 14cubic feet with pure CO2.. (Remember thats theoretical if it all reacted instantly)
So you want to dilute that 500-1000x giving you 7000-14000cubic feet of ideal air..
Now a typical closet is probably just under 50 cubic feet, so that works out to 140-280 exchanges of air..
Like I said fermentation time depends on skill as much as dope growing, so 5-10 days is doable for a beginner where as experience can take that down to 3days..
Assuming 5 days, that allows you to exchange optimum air 2-5 times/hr (12hr flower day)..
Heck, thats not that bad for a small space If scaled up a bit.. If engineered properly it actually might do well, and would definately help..
Cost would vary depending on what you're fermenting.. I'd go with 90% sugar, and 10% molasses for nutrient, and flavor, with a bit of diammonium phosphate for speed.. $1/day investment would atleast make a difference in a closet setup I think..
Bonus is, you get some alcohol to drink/distill (that would be a light rum btw after distillation)..
What does it cost/day to run a bottle? If I was bent on CO2 I'd probably want a bottle with gadgets, but I'd definately ferment in the same area.. I guess the final bonus would be odour disguise..
*Its 2:30am, all that math was done in my head.. Sorry if I goofed
*A mole is like a dozen.. A dozen is a word that means 12, a mole is a word that means 602000000000000000000000 (6.02*10^23).. Its just used in chemistry like a dozen is in a bakery
*Yeast is temperaturedependant.. Fastest at 80-100°F, nearly dormant at fridge temps, dead at just over 120°F.. I dunno if chilling it nightly wouldscrew it or not..
*You can add yeast from previous ferments instead of new stuff.. There is a bacterial limit if you're drinking it, but its beneficial actually if clean and not too old..