Jason both your suspicions are correct:
1 you cannot backup a database that is set offline;
you simply get this error:
Msg 942, Level 14, State 4, Line 2
Database 'MyDatabase' cannot be opened because it is offline.
Msg 3013, Level 16, State 1, Line 2
BACKUP DATABASE is terminating abnormally.
2. yes,you can restore over-top a DB that is in an offline,WITH REPLACE.
The advantage when it's offline, is there's no way for a fast-connecting application or user to reconnect to the database when you are trying to do a restore process.
setting a database to single_user or restricted_user still leaves possible avenues for connecting to the database, which can interfere with a restoration process, especially if it was scripted and assumed to be able to complete without any errors.
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