Yes. Facebook supports desktop applications, but they must go through a special authentication mechanism. Essentially, the user will need to be directed to facebook through a web browser window as part of the authentication process.
Here is the documentation on the authentication process: http://wiki.developers.facebook.com/index.php/Login_Desktop_App
There is a relatively polished Java library for facebook here: http://code.google.com/p/facebook-java-api/
If the Java library above does not meets your needs, you can build an implementation on your own. Essentially, you will need to interact with the Facebook REST server, as described at the top of the page here: http://wiki.developers.facebook.com/index.php/API
Edit: After doing some more research I have a few more resources to provide:
Here is a list of some applications written using Java for facebook:
http://wiki.developers.facebook.com/index.php/Facebook_apps_written_in_Java
And there's even a neat desktop application that is open source here:
http://code.google.com/p/fb-photo-uploader/
Good luck!