Just recovering from all the people above who have no idea what they are talking about.
The people who think CO2 is going to pool in a layer on the floor or think CO2 isnt absorbed by roots make me laugh.
Most people have a sealed water system to fight humidity so the CO2 is going to all be retained with most of it being absorbed by the roots.
I dont know if carbonated water is what your going for I was more thinking a fermenter bubbling into the water... the majority of the CO2 is going to be absorbed by the water or reabsorbed anyway (Im thinking about a bubble bucket type system).
@Martha 'Maybe foliar feeding with CO2 enriched water would be a better idea, or has this also been tried?'
I think this is an idea but wouldnt be very effective and might burn the leaves if your not carefull with too high pH.
If your struggling to understand this concept have a look at what aquarium growers are doing with CO2 enrichment in water with fermenters.
Also iv briefly thought about the acidification issues of adding CO2 into the solution and dont think it will have a major or any effect or might be used benefically by people with issues of rising pH, however the pH should lower as you add CO2 but rise again as the CO2 is absorbed?