America's Test Kitchen actually does suggest adding water to reduce the amount of time needed for caramelization--and not an equivalent amount of water, but much more than the amount of oil you'd use.
The idea is that adding water, raising it to a boil, and covering the pan reduces the amount of time needed to raise the temperature of the onions to the caramelization point, more than offsetting the amount of time needed to remove the water itself. That plus adding some baking soda near the end reduces the overall time considerably.