I used Dawn to strip off all the wax present on my car after delivery, before giving it the Zaino treatment and yes, it does a fantastic job of this.
If you want to test it, wash your waxed car with Dawn (or for the UK guys Fairy Liquid) and then rinse with a gentle flow (not spray) of water.............notice how it easily sheets-off the bodywork and the water doesn't bead; a good indication that the surface is hydrophilic and bereft of wax. Believe me, there is science behind the formulation of car shampoos; you are not being ripped-off (most of the time

).