Its a worthwhile question...
To get a bit more into the idea behind why it doesn't work: For CO2 to really work effectively, the CO2 levels need to be CONSISTENT for the plants to get the best benefit. Adding CO2 via pressurized systems or yeast can keep levels (relatively) constant throughout the entire photo period, as they continually pump CO2 into the tank. As some of the CO2 is used and some gasses off, the system replenishes the supply. On the other hand, fluctuating CO2 is an invitation to all sorts of algae.
The easier alternative and more than likely the far cheaper alternative would be 'liquid carbon'. Its a solution containing glutaraldehyde a carbon polymer that allows plants to absorb the carbon from the water column that way. This can be done as a single addition daily, because the glutaraldehyde remains in solution of the water for about 24 hours. But, the CO2 being added by a single addition like with sparkling water would not leave much CO2 in the water at all, and would quickly 'fizz' away. It would certainly add some CO2 to the water and some that would allow the plants to uptake it. But, what it would more likely cause is algae problems that you would rather not deal with.
Downside to glutaradehyde: It is poisonous to some plants, vallisneria and elodea, for example. The benefit is that it can also be a poison for algae as well. I've had a bit of success training vallisneria to cope with the additions of the glutaradehyde by starting with a lower dose than the recommendation and slowly increasing it to the full dose level over a period of weeks.
