If you live in a hot climate, as many (but not all) deserts are, then you might not have any antifreeze in the radiator.
I live in an area where it gets well below freezing in the winter, so antifreeze is used then obviously. However, I have used straight water in the warmer months and I have heard of people in warmer areas using straight water all the time. I have also put water in the windshield wiper reservoir before.
If you are going specifically to a hot desert and you are already survival-prep minded in advance, then drain your radiator before the trip and replace it with water. Then again, if you are so minded then please bring 5 or 10 extra gallons of water just for drinking as well. This is one of those situations where those who aren't prepared aren't going to be ready to use their vehicle as a drinking source, but if you are prepared to do so then you probably won't need to because of the fact that you were better prepared.
Thanks to @bob for the comment linking to mechanics SE. Even though some people do run their vehicles with straight water in the radiator, apparently manufacturers discourage that even during warm weather since the antifreeze has other benefits than just lowering the freezing point: it also raises the boiling point and helps the parts to last longer.
If that concerns you, then don't run with straight water all the time. But if you are so concerned about emergency water rations and want every option possible available to you, then you should be able to do your desert trip on water then switch back after.
@bob also mentions antifreeze residue and suggests flushing that out after draining the radiator if you do this. I doubt the residue would kill you, but I'm not certain and it can't hurt.
If you can find anything with moisture in it - animals, bugs, plants, whatever - and if you have a plastic bag then place your moisture-laden objects into the bag and place the bag in the sunlight in the vehicle with the doors and windows shut. This is to help evaporate the moisture out of the object and condense on the bag.
I have done this with plants before, and got a small bug usable amount of water from them, an amount better than nothing. It was not in the desert, but if you can find anything in the desert then try it.
This is not exactly what you asked for, but it is still using the vehicle to help keep you hydrated so I think it's in the spirit of the question. Of course, you could try it without the vehicle, but I think using the vehicle as a greenhouse is going to help speed up the water extraction process to make it a more viable option.
I hinted at this above, but it deserves its own section.
I would avoid this the vehicle fluids route altogether, even the radiator part I mention above. If you do not remember enough details and you only remember "Oh yeah, this one liquid in the vehicle was supposed to be drinkable if I get the contaminants out. Maybe I'll be ok if I distill it" then you could get yourself into trouble.
Since the vehicle fluids are only guaranteed safe if you remember all the details and prepare ahead of time, we can safely assume you are putting survival-prep effort into the trip. If you are putting the effort in, then you might as well apply that effort where it will have the greatest effect.
Here's an analogy: if a car is coming your way, driving on the sidewalk, and you take the time to put on a helmet thinking it will help your chances of survival and you ask someone to toss you their elbow and knee pads, then someone should rightly yell "Jump out of the way!" instead as that action accomplishes the goal of surviving much better.
Here, you need to prepare anyway to be able to make use of the vehicle fluids in the manner you have suggested. If you are preparing anyway, a much better prep is to simply bring drinking water with you. If I were driving across desert wilderness, I would bring at least 2 containers that held 5 or more gallons of water. I bring a lot of water on multi-day drives even when not driving through desert or wilderness.
If you want to do something to help you beyond just bringing water, rather than thinking ahead of time about the vehicle fluids I would bring multiple plastic bags or tarps and a shovel to use the desert solar still method of capturing drinking water. You could bring an entire roll of trash bags which could be light weight and take up little space, and a bunch of solar stills would probably provide more drinkable water than processing vehicle fluids, and the water would be more trustworthy.
The knowledge and effort you would need to put into benefitting from vehicle fluids is so great, and the benefits so small compared to any other method, that I would not consider vehicle fluids a reasonable survival strategy. Even if possible, I would consider it such an unreasonable strategy (and dangerous) that I would not bother to prepare for it even if I expected my car to die in the middle of a car graveyard with lots of vehicle fluids. Even then, I think you'd be better off with other preparations.