Yes, but before you do that, you need to register the card with American Express (add your name and billing address to the card). This is necessary because the online merchant will then be able to match the name and billing address you provide for your order with the name and billing address on file for your visa gift card (just like they do for credit cards). Should they be unable to match your information, your card may be rejected.
If you are trying to use your American Express Gift Card on eBay or link to PayPal, that may be more challenging. With regards to PayPal, it depends on whether PayPal requires you to go through their verification process. If they do, then you will need access to your transaction details. American Express allows you to view your transaction details online if you register your card. You will need the special code PayPal sends to your card to be able to successfully complete the verification. If you are successful at viewing your gift card transactions, then you will be able to link to PayPal, otherwise, you are out of luck.
This info was obtained from http://blog.giftcardrescue.com/2009/03/27/american-express-gift-card-explained/.