That would imply a wet-bulb temperature of over 40 C, which shouldn't be survivable. Does everyone spend all their time indoors? What if there's a power outage?
Of course Dubai's skyscrapers wouldn't be very well suited to this method so yeah, they'd have a problem in this situation. I've been there during summer and merely standing outside is very tough on the system. Of course as a wealthy European that was only a mild inconvenience as you move between the overcooled mall and the SUV. Now if you're one of these modern slave workers coming from poorer countries and tasked with digging a ditch outside or something like that, it's probably a different story...
Yes, you must remain indoors in non-evaporative air-conditioning, dehumidification or near sources of cool water, or you die.
Power outages? People can die.
You can also have high-mass buildings that you shut up during the day and ventilate over night. This is the traditional approach, and works well if the night temperature is a lot lower than the day.
And this is why the existence of Dubai is a testament to the hubris of humanity.
(The population is composed of just 15% native residents, with the remaining 85% being composed of expatriates, see http://worldpopulationreview.com/world-cities/dubai-populati...)
Houston didn't really take off until the invention of air conditioning but even when my house was built people engineered around it. When first purchased my house had a number of shade trees because blocking sunlight is extremely effective. Every room with the exception of one bathroom has multiple screen windows to facilitate natural airflow through the house. That one bathroom still has two doors and a window to help with air movement.
In addition there is a whole house fan that draws air from throughout the house to the attic. This helps both exchange air when people want air movement which is cooling and also helps move heat out of the attic which is coming from a blazing hot roof. The attic itself is nearly the same height as the floor below it and each end of the attic has huge slatted exhaust ports. They are easily four feet wide and seven or eight feet tall. They are needed because the whole house fan can draw hard enough to break a window, or so I've been told.
Although the house was designed to breathe and move air because it was all they could do to combat the heat these days I shut all the windows and run the air conditioner. I may be a fan of the architecture but I'm not a fan of the lifestyle. My friends in sealed houses have much lower energy bills, but if my power fails I can at least open the windows.