When you boil water (just like when it evaporates out of your tank) it's pure water that you boil off.
You could boil tap water, and collect the steam into a container where it would cool and condense. That would be pure water.
Unfortunately, it would be extreamly inefficient to do it. The amount of energy to boil a gallon of water like that would cost far more than just using a ro/di to begin with.