I have just started to use the synchronisation functionality available within Emby and noted a couple of points that render it almost unusable as a solution for my scenario!
I use the Android app on my tablet and, as expected, the items that have been marked for synchronisation do copy down to the device correctly. The first problem is that they can only be copied to internal storage which means there is a severe handicap on the space that can be used. I tried to change it to SD card; however, it would seem the app is not requesting the appropriate permission (an example of an app that does do this correctly is Solid Explorer).
The next problem comes when trying to use the app in a location where there is no network connectivity available. I currently have to browse to the file using a file explorer app and also use a video player app. On top of all this, I am required to manually mark the item as watched the next time I use Emby with network connectivity.
Please enable an offline mode which will queue the watched and resume statuses for local items to the server on the next available connection!