R77.30 Management database is in fact a bunch of text files with description of policies, network objects, users, groups, protocols and services, etc.
The structure and dependencies with these files are complex, as some changes are saved directly when you edit and save changes, and some others are done only when you prepare a FW policy for compilation.
One of the reasons to install database may be related to log management. When you create a new object, it will not show up on the logs as such until you install database on the log server.
Management Sync is a completely different matter. It is a process to dump the current state of your Primary Management Database to the Standby Management server. It has nothing to do with DB status, although there is an option to trigger management sync automatically after each policy or DB installation