If you're doing large scale evap cooling in the Sonoran you're just removing water from an already stressed water table. I'd say put them somewhere cold and do district heating during the winter.
Does district heating actually work for heat from data centers? The exhaust temperature of computer equipment is only slightly above room temperature and the structures in need of heat would only be at slightly below room temperature when calling for heat. Heat distribution systems with tiny differentials like that tend to have poor efficiency, i.e. you're going to have consume a lot of energy on fans/pumps.
Meanwhile in a cold climate you can do cooling by just blowing outside air through a filter, so the alternative in those climates is that rather than running a compressor.
That kind of district heating already exists and it uses heat pumps to raise the temps. Basically you run a huge AC somewhere and dump the hot side not into air but into district heating.
That's actually not that bad. Then it's no longer "free" but it would be more efficient than running heat pumps against the cold outside air, and then you could run them in reverse during the summer to cool the data center.
I'm not a geologist but...does evaporation remove water from the water table? Where I live, my understanding is the answer is "no" because the vast majority of rain water is deposited in our groundwater. Things like agriculture are dangerous because the answer is "yes" - you're literally shopping the water away as an agricultural product.
Another dumb question: why are we building projects that need tons of power and water in the Sonoran desert instead of next to the Great Lakes
It at least removes water from the local water table.
You pump water up from the local water table to run your evaporative cooler. The water evaporates. But the air was at 10-20% humidity. The water from the evaporative cooler will raise the humidity, a little bit, but not enough to make it rain. It may make it more likely to rain somewhere downwind a few miles, or a few hundred, but not here.
For your second dumb question: At least some of the Great Lakes have at times had issues with water level. (They want enough to allow ships to pass between the lakes.) The upside is, there the humidity is high enough that you're more likely to get the water back in the form of increased precipitation.
Depends on the aquifer. The assumption you're making is "natural precipitation recharges aquifers" and that assumption is not always true.
Sometimes it's true, but it takes 10,000 years so if you mean "recharges while our current civilization exists" then it's effectively false. This is the case for the Ogallala aquifer which supplies 27% of the irrigated land in the US.
Sometimes it's just completely false because the groundwater exists as a sealed bubble of water put there during the last ice age. That glass of water you just drank? Congratulations! It's 25,000 years old, and we know this through isotopic analysis. Your drinking water was mined and once it's gone it's gone forever.
So it's complicated. Generally speaking, deeper groundwater sources take longer to recharge if they recharge at all. I don't know the particular groundwater situation around Tucson.
> why are we building projects that need tons of power and water in the Sonoran desert instead of next to the Great Lakes
Evaporative cooling is effective and cheap where humidity is low. It doesn't work well where humidity is high.
> Things like agriculture are dangerous because the answer is "yes" - you're literally shopping the water away as an agricultural product
Very little of the water used to grow the product actually ends up shipped. For example with alfalfa (a major Arizona crop) only 0.005% of the water used to grow it end up in the alfalfa. The rest of it first ends up in the ground near the plants or in the atmosphere near the plants.
This is also the case for most high water use industries. For example making integrated circuits uses a large amount of water but very little if any actually ends up in the chips themselves.