The main problem with carbonated water is the sodium.
Plants don't like too much sodium (also too many minerals--this depends on the species of plant, obviously).
that being said, plants need N,K,P and micros to grow. The level of CO2 and light are also important.
FWIW, emersed growth isn't necessarily the fast way to grow aquatic plants. My HC grows faster immersed than emersed. Emersed growth is easier to maintain (fewer algae problems, etc).
CO2 is also an issue. emersed growth does not need ferts or CO2. All you need is a nutrient rich substrate.