Using app access token had previously been asked in this question (How to use Facebook appAccessToken with Spring Social) and Craig Walls gave a good explanatio
You do not need to fetch an app access token - you can actually use the app id and secret separated by "|" as the access token. - You can see it at the bottom of the app access token section in the documentation: https://developers.facebook.com/docs/facebook-login/access-tokens#apptokens
Spring Social's Facebook API binding does not (yet) support v2.0, but that's something I'm working on right now...so hopefully soon. Once that's complete, there'll certainly be some operations that work only with user access tokens and some that only work with app access tokens, and some that will work with either (FWIW, Twitter's API has a similar set of circumstances).
Keep an eye on the project in GitHub or follow @SpringSocial on Twitter to know when the v2.0 stuff is available. (I'd appreciate any help I can get in testing it.)
Although it makes no sense at all to obtain your FacebookTemplate via the connection framework for app token requests (connections are, by nature, a user-oriented concept), you can always construct a FacebookTemplate wherever you need it, giving it an app access token obtained via OAuth2Template's authenticateClient(). You can certainly do that now with the v1.0 API binding, but I'm uncertain what ops an app token would work with.
FWIW, as I'm working on the v2.0 API binding, I'm starting to sense an opportunity for FacebookTemplate to carry two tokens: A user token and an app token. This way you can perform app-centric requests even from a FacebookTemplate obtained from the connection framework. Then the only time you'd ever want to construct a FacebookTemplate manually is if there are some operations for which either kind of token will work, but the results would be different depending on what type of token is used.