There are a couple different types of water softener systems, using different ion-exchange substrates (Potassium permanganate is another common one). Generally, as WH pointed out, the goal of a water softener is to remove the minerals that form scale or deposits on your ceramic fixtures. However, the ion is exchanged with a Na or K ion in these systems. The resulting salts are more soluble than minerals such as lime, so they don't damage your tiles, but plants FAR prefer the minerals (in moderation, of course!).
So if you are choosing between tap, softened, or distilled/RO water, you may very well be better off picking up a RO machine to further purify your water, or running tap water 'cut' with distilled water to bring the total hardness down to a more acceptable level.

Since you are running hydro, your best bet is an RO machine and then run with added CalMAg Plus to add back a CORRECT level of trace minerals for your plants to enjoy.