No, you cannot complete the entire tax-free shopping process at the airport.
To receive a tax refund through PIE VAT, you must apply for tax-free shopping at the store or a tax-free counter in the shopping mall when making your purchase, and complete customs verification at the airport or other departure port before leaving Japan.
If you have not completed your tax-free application at the store or tax-free counter, you will not be eligible for a tax refund, even if you complete customs verification at the airport.
Please make sure to complete your tax-free application at the store or tax-free counter when making your purchase.