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 have found that new dishwashers with good eco ratings leave easily detectable amounts of soap on the dishes. Even apart from any health impact, I make it a point to never use them on their default eco programming, but switch to sth that uses more water. I want my dishes clean, that includes soap residue.
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.
Use less soap. I use about half as much and the dishes come out fine. I've had better luck with liquid based soaps too as they mix immediately with the 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.
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.