Yes, the application works in offline mode, but many users considered this as being an issue. Technically, the offline mode activates itself when there is a problem reaching the update servers. The fix is by re-installing the application. If you disconnect from the Internet, the application will work in offline mode.
If by offline you mean "without Internet", then yes, the application will work that way too, but the updates need to be applied manually.
Download updates: http://www.avira.com/en/support-vdf-update-info