Depending on what kind of soap it is, the effects may be limited to a slight surfactant effect. There's no reason for car wash soap to be antibacterial, so I don't think it would cause any harm.

I'd probably drive the car onto the lawn to wash it in order to save as much water as possible.

garett, I always wash vehicles (3 of them, occasionally all on the same week-end) on the lawn. I use whatever is in the laundry room at the time ("Tide" usually) and recycled water. I count it as a lawn irrigation and like to think that I am conserving water. My chief worry are the oil, grease and 'traffic film' products that are rinsed onto the grass. But then I remind myself that turf is a good filter for these products and they are better here than in the storm water system. Thus I am consoled.

Dishwashing liquids are detergents which are harmful to the environment in themselves.