We're afraid not. This is clearly defined in Section 7 of our Contract:

[ALL SALES ARE FINAL]
AZC, by contracts with the registrars with whom it does business, is bound not to cancel a registration request once it is submitted. Therefore, all sales from registrars to AZC are final. In turn, all sales from AZC to the Customer are final. There is no refund under any circumstances. AZC provides the Customer with final verification tools prior to the final order confirmation. It is solely the Customer's responsibility to properly verify all data submitted. By clicking on the [Order Confirmation] button, the Customer warrants that all information tendered in support of the application order is valid and correct. AZC makes every effort in the signup process to alert a Customer of such consequences. It is the customer's responsibility to assure the accuracy and desirability of the domain name submitted to AZC.