I home water softener doesn't put any salt into the water. The brine tank is used to clean out the elements in another tank that remove the unwanted stuff from the water. Think of the other tank similar to a carbon filter. It absorbs and absorbs the stuff you don't want, but then it is "full." That's where the salt tank comes i n. The salt water is then used to flush out, or clean, the stuff in the other tank so that it can start absorbing the "bad" stuff again. So there is no actual salt in your water.
However, I was told that water treated by my softener is NOT the same as soft water in the tank. (I thinka mod here told me that....but I can't remember who). I was trying to soften the water in my tank, and was told to use RO water instead, along with a Kent product or two to replace the minerals that were removed in the RO process. HTH.