From my tests:
1) In mode "Offline if online startup failed" without using "of_checkupdate()"
The application is updated automatically, the database never (this seems logical).
2) In mode completely Offline
From a stable point (app and database updated), if I modify the database only, the function "of_checkupdate()" returns:
- For an "Incremental application deployment": 3 - There are updates for both the database file and the application
- For a "Full application deployment: 3 - There are updates for both the database file and the application
- For a "Deploy already generated application": 1 - There is an update only for the application.
I have not gotten that the function returns the value 2 - There is an update only for the database file.
3) In mode "Offline if online startup failed" and using "of_checkupdate()"
The application is updated automatically and, when it start , the function of_checkupdate() return "2 - There is an update only for the database file".
It seems we have covered all possibilities 
Regards