Ah, well, it turns out … there’s a bug in the basic “include folder for offline” GUI, whereby it is COMPLETELY IGNORED for certain folders. One of those folders being … the magic “All Mail” folder in Gmail.
“Right click on the account in the Folder pane, and click on Subscribe..
You can then tick or un-tick the subscribe box for each folder.
Click on OK when you’ve finished.”
This seems to work, having just tried it. Although … I also went into my profile and manually deleted the monstrous All Mail file – but before I did the above hack, TB (dis)loyally would immediately start redownloading that folder each time you started it up. Now it merely downloads the headers (at least that’s counted in MB, not GB). Now you can have your email client, with about 4 pages of manual hacks, work as … a basic IMAP email client.