Excerpt from an article on Professional Car washing, there appears to be no benefit to using RO in the wash cycle and it may even be a detriment:
"Since RO water reduces surface tension beyond that of softened water, it has nothing but negative value when used with polishes, sealers, clear coats, hot waxes or drying agents. There are some misconceptions that drying agents can be added to the RO rinse. Why would we remove 3-400 PPM (parts per million) of mineral solids from water to make it RO pure and then put 2,000 PPM of wax solids back into it?
Some might consider using RO water for the entire wash process. From a presoak and detergent standpoint, there is no positive benefit to using RO water in place of soft water.
First, the soluble sodium salts left in the water after softening have no detrimental effect on cleaning. Also, RO water can reduce the foam level of friction foam detergents and touchless presoaks.
The RO water apparently interferes with the bubble formation dynamics causing the bubble wall to thin out faster because of intense surface tension reduction that breaks the wall formation of the bubble.
If softened water has no known value in the high pressure rinse cycle, then neither does RO water. Considering the water volume, the cost is very high and unnecessary. Leaving a residue free rinse water surface has no positive value for subsequent wax cycles."