Well, doing some more tests I have concluded that the feature is actually working for the most part. My problem was I still didn't have offline storage enabled for the "system" labels: Inbox, All Mail, Sent, Drafts, etc. Now I can go to gmail site and put a label on a message in Inbox, e.g., toplevel2, and I go to toplevel2 folder in tb and see the message there too. When I click on the new message in toplevel2, no download from gmail occurs since the message is fetched from Inbox's offline storage. The offline storage file for toplevel2 remains empty. However, if I copy a message from Inbox to toplevel2 with tb, the offline storage for toplevel2 now contains the copied message; but another download (actually imap fetch of body) doesn't occur. So you don't get a redundant download but you do have redundant storage if you do a copy in tb. Another thing; I have done the above tests with autosync disable in preferences. I need to repeat the tests with autosync enabled, which is default. Also, I only tested with mbox offline storage format and not maildir.
Bug 1554529 Comment 9 Edit History
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Well, doing some more tests I have concluded that the feature is actually working for the most part. My problem was I still didn't have offline storage enabled for the "system" labels: Inbox, All Mail, Sent, Drafts, etc. Now I can go to gmail site and put a label on a message in Inbox, e.g., toplevel2, and I go to toplevel2 folder in tb and see the message there too. When I click on the new message in toplevel2, no download from gmail occurs since the message is fetched from Inbox's offline storage. The offline storage file for toplevel2 remains empty. However, if I copy a message from Inbox to toplevel2 with tb, the offline storage for toplevel2 now contains the copied message; but another download (actually imap fetch of body) doesn't occur. So you don't get a redundant download but you do have redundant storage if you do a copy in tb. Another thing; I have done the above tests with autosync disable in preferences. I need to repeat the tests with autosync enabled, which is default. Also, I only tested with mbox offline storage format and not maildir. Edit: Test with autosync enabled again (default setting) and still works OK. Haven't tried maildir storage format yet.