Jeff is right on. You will damage the pool if you cover it in the AZ heat. We lived in Surprise and my husband is a commercial pool builder. Consult a local pool company. I would recommend Shasta. They can tell you what the pros and cons can be.
Best of Luck,
There is a company that will come to the home and build a structure within your pool that will convert it to a patio and storage container.
It's a framed in structure and they can make it look great.
Here is the company web site: http://www.deckover.com
All The Best!
Stew Keene - Home Smart Realty
Certified Short Sale Negotiator
Arizona Real Estate Professional
Yes you can put a cover on it. However the pool plaster will crack without water in the Arizona heat. The cost of the pool repair may be extensive when/if the cover is removed. Unless you never plan to use the pool again or sell the home with a pool, covering the pool may be a good idea.
Less expensive solution and a more functional yard, would be to buy a home without a pool.
There are covers you can walk on and a few pool companies that provide this. They would have to confirm the maintenance component.I can give you my pool guys number if interested.
If you won't use a pool though why pay for it?