Watering is always required if one wants the trees to uptake nutrients (it's the action of the water evaporating through the leaves that pulls nutrients up). In times of drought, water is going to be absorbed from deeper portions of the soil, which is typically less nutrient dense. Also, conventional fertilizers come in slow release form, which would act similarly to organic.
Water isn't required for mangoes (here in FL) if one is only interested in keeping the trees alive. For bountiful crops of quality fruit, moist soil is important. In places where rainfall isn't as plentiful as FL, only the most drought tolerant species will survive without supplemental irrigation (eg, eucalyptus).
In life, optimal outcome is generally achieved via finding a "sweet spot" or middle ground between two extremes. A mix of organic and conventional practices works very well. The extent to which one can move to one side or another of the spectrum depends heavily upon what natural amenities the growing location provides (eg, natural soil quality, rainfall, temperatures, disease pressure, wind, etc).
I’m all for watering as needed but with Mangos at our place it is not needed. Grafted Black Sapote and grafted Sapodilla are a different story unless the soil is perfect, which on a larger scale takes time. Seed grown trees of BS and Sapodilla don’t require watering, for this reason we are growing replacements for BS and Sapodillas out now. We plan on not selling our Mango fruit for the next 2 years and we are planting out all our Mango fruit seeds. A major difference between organic and those using chemical fertilizers is you have to water if you use chemicals, whereas if you are organic watering isn’t always required especially for Mangos here. Grafted trees just don’t have the vigor of seed grown trees.
The Pickering is a 5x5 mound in ground two years never been watered.
