Is it possible to make the application run in the background without the use of the Taifun Batery extension?
The battery manager extension itself does not run in the background… you probably have seen Battery checker reminding you to unplug when fully charged - Tutorials and Guides - MIT App Inventor Community which uses itoo together with the battery manager extensión
Generally to do something in the background try
What about elaborating a bit what exactly you are trying to do, so we can give better advice?
Taifun