In a scenario where you've filled the place with people, the interior humidity is going to exceed that of the exterior air and you'd just start dumping the moisture outside exchanging with the fresh, dryer air. It's a comfort regression sure, but not a everyone dies situation.
The survival of the people doesn't come down to the AC heat pump keeping up, it comes down to supplying them enough water to drink and disposing of the humidified air.
My point is just that it's the relative humidity that matters, and the AC system has some options there. I've lived through a desert summer in a small space without any AC at all. I'd just keep the windows closed as deep into the day as possible riding out the night's cooling until the air gets too humid indoors from sweat and respiration for the fan to have any cooling effect. At that point I'd open the windows for relief. The air coming in was usually much hotter than the interior air, since the space was well insulated and nights get cool, but it didn't matter because it's very dry air and perspiration resumes functioning. The situation is easily survived unless you run out of water for your person.
Of course if the outdoor air is something like 100% humidity there's only the heat pump option, but that simply doesn't happen in deserts when it's hot out. It's a desert, not the tropics.
In the desert the relative humidity shoots up when it cools down, the humid nights are the worst. But it's because they cooled down. Again, not a survival problem since it's not that hot, just uncomfortably muggy. One saving grace with deserts is they don't generally have any mosquitoes, so these humid nights can easily be spent outdoors without any annoyance.
That's equivalent to opening a window without the AC doing anything. If that would work we wouldn't be in a "crowd everyone into a shopping center" type situation, the people would be just fine outside in the shade.
> It's a desert, not the tropics.
While half of India is in the tropics, this part indeed isn't. But next month the monsoon will put humidity at approximately 100% [1].
1: https://en.climate-data.org/asia/india/delhi/new-delhi-30/
Even when the air temperature at your fresh air intake is cooler than the air at your condensor coil? Wouldn't we assume no system would draw its fresh air from near the condensor coil?
You still have a heat pump in the system, and there's a temperature difference between the air inlet and the pump outlet.
Specifically the ambient indoor air heat is absorbed by refrigerant which is transformed into a superheated vapor saturated with moisture. When this vapor either touches a cooler surface, or has cooler air blown past it, it will dehumidify and exhaust the heat it has absorbed indoors to the outside. The mechanical work done by the AC (fans, pumps) is also being released as heat. So the total energy being dumped outside is therefore the heat that's taken from the inside plus the energy used by the AC released as heat.
Humans burning calories to stay alive creates heat, and thermodynamics that you spend energy to remove it or see the temperature rise. Whether that heat is hot air or bound as humidity shouldn't make a large difference.
You can see there that even at extremely dry conditions, if the operative (ambient + radiant) temperature is hot enough, it will cause heat discomfort. Even if the human starts sweating, that'll only reduce the temperature a bit so dehumidification isn't the only role of air conditions, sensible cooling is also a factor.
The principal human-appreciated effect of AC is the dehumidifying of the air when it's cooled.
The dry interior air allows human perspiration to regulate temperature effectively. The AC doesn't have to cool all the bodies, it just has to keep the air dry enough.