I guess if it mixed with the water, it could. I remember Amano saying he originally was struck by the idea of using carbonated water for this purpose, but was concerned about 'other' stuff in the water.
As long as you could remove the alcohol (which I would think is toxic somehow to critters.plants), and any other bad things, it would work.
In small doses, it's apparently not toxic to fish or plants at least in sw tanks. People do this for sw tanks to boost populations of bacteria to remove nitrates and phosphates from the water. If you removed the alcohol you would be adding nothing...alcohol is the source of carbon. I was just wondering if it would be useful to plants or if it would just get used by bacteria. Sugar and vinegar are two other things that are commonly used for this purpose too for the same reason. I can't find any info on anybody trying this in a fw tank, probably because it wouldn't work to reduce nitrates and phosphates in that setting.
Adding carbonated water would just be adding small doses of co2...likely not very effective as it will evaporate pretty quickly anyway. Methanol, on the other hand, would not, neither would sugar or vinegar.
If I had a plant only tank, I'd give it a try. Personally, I would lean away from trying it in a tank with fish. I remember seeing a video as a kid of a fish tank into which alcohol had been added -- poor little fish were swimming upside down. Maybe us humans can handle losing a few brain cells now and then (debatable), but a fish brain starts out fairly small in the first place.
I highly doubt that very tiny concentrations would harm fish, in fact I know it wouldn't, but the key is tiny. In SW tanks the dosage is something like 1 ml of vodka for a huge tank. SW fish and corals tend to be far more sensitive than most fw fish, and they do well and corals actually improve due to the subsequent nutrient depletion. So I guess the question is firstly, can plants use it, and secondly, is it of any use in doses that are small enough so as to be not harmful to fish? And perhaps thirdly, will it cause any unwanted effects such as massive overgrowth of bacteria which could harm fish secondhandedly due to oxygen depletion? Putting fish in a very concentrated vodka/water solution will kill them, it's one way to euthanize a fish. And yes, the fish will go upside down, but we're talking far, far higher levels than what people dose to SW tanks. But if it has the same effect as it does in SW tanks, that of causing a bacterial bloom instead of staying in solution for the plants, if indeed the plants can use it, it wouldn't be very useful. I'm not really sure how to measure the beneficial effects of something on plants, so I'm not sure if trying it is even worth it. Probably what I need are some fast growers and high light (to see effects quickly) and a control tank of course. I might be able to do this if I can come up with enough tanks. Really, three tanks would be nice (0, moderate dosing, higher dosing). Maybe even three 1 gallon containers would be enough to try something.
Just did some research (with my limited understanding of chemistry) and it seems to me that it's probably unlikely that plants can use the carbon in ethanol. The bacteria that seem to use it are evidently bacteria that get their carbon from carbohydrates and proteins (like us), not carbon dioxide, such as plants do. There are bacteria that get their carbon from co2 the same as plants, which is what was confusing the whole thing in my mind (such as nitrifiying bacteria which use co2). But I didn't realize there were so many variations in how different bacteria function. So if the bacteria that use ethanol do not use co2, the plants that use co2 wouldn't use ethanol, I guess, if my logic is right.