In a closed system sure, but I'd expect a larger building to have significant fresh-air return systems.
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.