I craft coffee water from distilled water. With the cost of distilled water, I am thinking about getting an under-sink reverse osmosis system. Do under-sink RO systems normally produce zero Gh and Kh water - is the water equivalent to distilled in that regard? In case it matters: the source water will be softened, through a sodium based system, well water.

TLDR, Straight reverse osmosis water has practically no KH, GH or TDS, given that the source water is reasonably portable and not excessively hard. But, it depends. RO systems do not remove 100% of everything; so the product water is not as pure as distilled. Thus, the purity of the product water depends upon the source water. This is true even if your RO is downstream or an ion exchanger unit (water softener). The IEU will take out the hardness and substitute sodium or potassium ions, depending on which regenerative salt you use. In other words, if your source water is a given TDS, the "softened" water will still have more or less the same TDS, but of a different composition. Downstream from the IEU, the RO unit will remove a number of other things, even most biologics, nearly completely, but the TDS will be, roughly, the same as if the IEU were not there.
PS FWIW, what you propose is exactly what I currently use. Some years ago, I had a tabletop distiller, which I used for coffee and battery water, until we moved back ashore and left the distiller on the boat. You may wish to add a bit of hardness back to the water, just as you're doing with your distilled water.