This feature is probably not what you think it is, so read everything first.
When you login to an Exchange server with Outlook, it will pull your inbox down...together with all of the other inboxes you have access to. These are inboxes that you don't *own*, but that you have rights to access. You don't get notifications for new emails in these inboxes. They're just folders, really.
This is useful because I have ~20 inboxes which are not mine which I need to access periodically, just to check on things. I don't want to be notified for every single one, and it's also a pain to manually add 20 inboxes to Thunderbird.
For now I'm RDPing into a Windows server to access Outlook so I can do this, but it would be nice to have it in Thunderbird. Let me know if an existing addon provides this functionality, and I would gladly pay for it, even if it is proprietary.