A water pillow softener is just a bunch of ion exchange resin beads in a cloth bag. Put it in the tank and it will take up a bunch of calcium and magnesium and replace it with sodium. It works just like ion exchange resins in water softeners that people buy for their hot water heater, if they live in a hard water region. If they don't use a water softener, the hot water heater gets a lot of calcium and magnesium carbonate deposited on the insides of the heating coils, reducing flow through them as well as reducing heat transfer. Basically, you are exchanging Mg and Ca for Na, and to plants and fish that doesn't mean any improvement that I am aware of. Sodium bicarbonate is kind of alkaline, and too much of it is bad for fish and plants. Actually, the tap water where I live comes from wells that have water that is just like softened hard water. It is all sodium bicarbonate, with calcium and magnesium so low that I can't get any measurements with my test kits. The GH is 0, and the KH is 19. I don't like this water for my planted tanks, and so I try to collect rain water.
i knew theres always something fishy with new jerseys water. :lol: 
