The amount that ends up in the water depends on the hardness of the water.You may get trace amounts of sodium ions but it is a very negligible amount compared to the salt that goes into your brine tank. Your first post implied that all of the salt goes into your water supply. If that was the case your water would be extremely salty.
Having said that, we seem to have veered off course slightly from the intent of this thread. I do believe that water softener salt would be something you could use for other purposes if the SHTF. I put that out for the group for discusson.