Ok, several things.
Plants will actively use bicarb, not just CO2. This process is independent of the carbonate-bicarbon-carbonic acid-CO2 equilibirum process. Plants vary in their ability to utilize CO2, with many of the traditional 'hard water' species being much more adept at it, eg valisineria.
If you think about it, your argument implies that injected CO2 is unnecessary as long as KH is maintained above 0, which can easily be demonstrated to not be true. Your chemistry is not incorrect, but that just tells us that it's either more complicated than that, or it doesn't explain the process fully.
Second, sodium itself isn't bad for plants, as it's extremely common in nature. It's when you dose it in high amounts that TDS increases, which causes problems for plants. KCl will do this just as well as NaCl will., but is used less for practical reasons.