IMAP is NOT necessarily on your harddrive. you must tell your email client to save email for offline use. Otherwise if you loose your imap connection, you may not have all your messages.
To restore, you'll connect to the "new" or restored account and using the thunderbird interface, move the email/folders that you want into the account and after it is done, you'll have it all back. That's one of the benefits of IMAP. you don't do it by just "copying' the files on your harddrive.
make sure your thunderbird settings are configured to save ALL mail offline, otherwise you won't have it when you need it.