Err, no. App.net is a company in itself. Storing stuff on App.net may unbundle you from other services (if your apps add support for App.net file storage, which is unlikely), but you become subservient to App.net instead.
It isn’t a removal of control, it’s just a redistribution. As it stands, using App.net to host your files is no different to using Dropbox, with the exception that Dropbox already has an ecosystem of supporting applications ready and waiting for you to use.