Yes AutoZone can look up receipts in their database for up to 3 months so if it's only been 3 months since you've purchase the item or part from AutoZone then they can usually find the receipt for your purchase and may be able to take the part or item back without the original receipt.
I've always had the receipts though when returning a part but they did tell a customer once that they needed the receipt to return the part to them for a refund or exchange.
The part mus also be in good condition and not installed onto the vehicle or they will not be able to take it back.
So make sure you keep your receipts handy in case you need to take something back to Autozone or other parts stores to save any hassle.