Sync is able synchronize data even if the program interface is hidden/disabled. On OS X or Windows, you can minimize Sync UI down to tray - in this case the app will still be running and you will be able to pull back its interface at any time.
The Linux version of Sync employs Web Interface, therefore to run Sync headlessly, simply start the application without opening its WebUI.
The Android platform allows for apps to work in the background, therefore no specific configuration for Sync is required. Note, however, that task-killers or memory optimizers can kill Sync and thus stop all synchronization.
Due to OS peculiarities, background synchronization is unavailable on iOS and Windows Phone devices.
Also note that every time you shut down and then re-open Sync, all the folders in your instance of the app are re-indexed and get a new modification time. If you made some updates to a folder in an offline state, once you go online, these updates will overwrite all the changes made by other peers who remained online throughout synchronization session.