No. As they use very little water compared to hand washing a load of dishes. And... they heat their own water too. You can hook one to a cold water line and it will still heat up and wash the dishes.
OK, I see, even if it only needed water for one minute, all those 120 amp loads in the neighborhood would be on at the same time, not pretty! Sort of a one minute brown out. This is assuming the flow of each dishwasher turned on all the elements, as might be the case in cold water that is cold territory. People on public water here complain their cold water is 70°F in the summer!