Yes, you absolutely can test web apps locally that use Facebookâ€™s Graph API. Iâ€™ve seen a number of blog posts that tell you this isnâ€™t possible and that you need a a fully qualified domain name (FQDN) such as http://www.xyz.com. But, Iâ€™m writing this post to correct that misinformation.
Iâ€™d call this a best practice for testing Facebook APIs. It doesnâ€™t require an FQDN until you are ready to deploy the final app on a production server.