This app was created as part of a DIY car stereo project. It was based on a Odroid C1+ with Android 4.4 Kikat and it had no internet access and it couldn't update the time and date. The Odroid's version of Android is rooted, so you can do things like set the time which apps are not allowed to do without root.
This will work on devices other than Odroids. The device does need to have root access or it will not work.
You might have to turn off the network time updates to get this app to work. Just manual set the time to any time and the app will update it when it loads.
The app is setup as an accessibility service so it will start up when android boots up. All you need to do is enable it in the accessibility settings and it will automatically start o its own. There are no ads or anything at all that should require internet.
More info can be found here:
http://www.swampsoft.org/android/androidgpstimesync/androidgpstimesync.php