They supposedly used to, but nothing on their site says they do anymore.
https://www.americanexpress.com/us/content/card-benefits/extended-warranty/faq.html
https://www.americanexpress.com/us/content/card-benefits/extended-warranty/faq.html
1. How does the Extended Warranty work?
When you charge the cost of a covered product with your American Express® Card, the Extended Warranty1 will extend the terms of the original manufacturer's warranty for a period of time equal to the duration of the original manufacturer's warranty, up to one additional year on warranties of five years or less that are eligible in the U.S.