We could still have many clients logging in in local mode, all of which trying to update/create/delete a record.
How???
Your question is a good one. The answer depends on the purpose of client using local mode. Requirement doesn't give emphasis on multiple users in local mode. I agree that it is possible.
As per my requirement
The database and client must be started together in standalone mode.
The server program must run alone
The GUI and network client must run alone.
are the only musts.
With these musts your questions can be answered if a clear understanding betwen database and server can be made. As per my understanding server consists of database plus network server.
In standalone mode network server need not be started. But you can start it and a client can talk with it. As Inuka said it is not a must to do.
What I am worried is that do I brake the integrity of the system if I initialize network server in local mode. Depends purely on the purpose of having local mode. I believe local mode can assist in changing application configuration. In that case it is better to have only one user in local mode. Otherwise user's reach inconsistent state during configuraton changes.
Remember the requirement talks more about customizing configurables (still optional) than other issues.
Jiju