Should an AT&T iPhone work with cricket?

I'm looking to buy an iPhone 5, and I found one unlocked to AT&T. I use Cricket Wireless, but have heard that they use AT&T towers. Can I buy an iPhone unlocked to AT&T but still use Cricket?

Unlocked means the phone can be used with any compatible carrier…

If you mean an iphone locked to AT&T, then yes, the phone will work on Cricket despite being marked AT&T.

A misconception is that a locked phone is locked to the specific marked carrier, in reality, the phone is actually locked to the main company providing the cell tower to the company, since Cricket uses AT&T towers, all Cricket and AT&T phones should work on each others service.

Cricket uses AT&T Go network, the Cricket near my house will put in a Cricket SIM card to see if the phone works.
Unlocked should work with Cricket, AT&T, and T-Moblile