As long as the cars battery is easy to access and easy to replace then yes as long as you buy the battery from Autozone then AutoZone will replace your car battery for you free of charge.
If the car battery is harder to access or they have to remove a lot of other stuff to get to the battery then no they won't replace it.
But most car batteries are easy to access and Autozone will replace the battery for you without any additional charge.
I always have had Autozone replace my car battery for me even though I can do it myself but I'm there buying the battery anyway and they will replace it for me so I let them do the job.