Probably not. Most of the water runs off the dishes. A very thin film remains that evaporates in the dry cycle, and even at that a lot of it will bead up and run off completely.
I got rid of a perfectly fine 35 yo dishwasher that cleaned fine even without soap, due to heat and water use. I got rid of it because it was loud, but I always wondered if running it without soap was perhaps not as eco friendly as a modern washine using less heat and water.
I use either Cascade powder or the Walmart brand equivalent and only put a teaspoon or so of powder in the cup per load and a few dozen granules of powder on the door for the prewash.