An atmospheric water generator is a device that extracts water from humid ambient air. Water vapor in the air can be extracted by condensation - cooling the air below its dew point, exposing the air to desiccants, or pressurizing the air. Unlike a dehumidifier, an AWG is designed to render the water potable.
You would be better off either digging a well, Cistern, Or living near a river or the ocean, You are not going to get a lot of water your way, It might help you stay alive for a day or two longer but its not enough long term.
When you're talking about the theoretical you could be all over the place. I would recommend buying a 500 gallon cistern or 10 50-gallon plastic (HDPE) drums and set them to fill with rain water. If one is literally in the desert and can't have a well installed. I recommend moving. Keep bleach on hand. I think it's one capful per 5 gallons, and let stand for an hour. (double-check that.) Bleach and grain alchohol are both incredibly useful. Stock that stuff.
You could look into buying a wholehouse dehumidifier and set it to run outside, but I don't know if it would be worth the energy, esp. In a SHTF scenario.
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Any dry environment without water, would require much more energy to get humidity from the air, for example Las Vegas NV.
So it's almost never worth it from an energy standpoint.
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You could look into buying a wholehouse dehumidifier and set it to run outside, but I don't know if it would be worth the energy, esp. In a SHTF scenario.