The softener will actually make life much, much easier for your RO/DI unit and can extend the life of your filters. A good softener will reduce water hardness to zero ppm - all before reaching the RO/DI.
The softener has a chamber full of plastic beads. As tap water flows through these beads, the contact between them causes dissolved minerals in the water to adhere to the beads, leaving the water that emerges free of minerals. The beads will build up with minerals over time, so they must be cleaned off, or they will lose effectiveness. To do this, a brine solution (the salt) is flushed over the beads, which releases the minerals from the beads and the resulting effluent is then flushed down the drain. Any salt that appears in your water after this process is residual and minimal at best.
Hope this helps. IMO, you have a good landlord to offer this option for the home. Besides, shaving will be smoother and dry skin will disappear with use of soft water.