Yes. Some people do that. Carbonated water can have a low PH and thats why some people shy away. I did an experiment a couple of weeks ago where i fed one plant carbonated water for a week to compare it to the other plants which did not get it.
The plant that was given carbonated water (no sodium-very important), grew a lot more and the leaves were darker and very tough. I now just have a small 1.3 gallon jug with water, sugar, and yeast in my veg chamber to generate a little extra CO2.
Fresh air is the best, but indoors, its tricky.