The increase in Sodium (salt) levels in the water can be significant, especially when treating very hard water; therefore a water softener would be somewhat of a compromise when it comes to vehicle washing
A water softener does not remove the minerals (calcium Ca and magnesium Mg) that are responsible for ‘water spotting’, softened water tends to strip wax by increasing the effectiveness of detergents; the softener doesn't get rid of all the minerals. The only way to get truly "clean" water is distilled or de-ionized water
I think a pre-filter may be of some help, but IMO a water softner is unecessary in conjuction with a CRSpotless filter system