I found out that addon which is loaded to AMO will be updated as soon as newer version of addon will be uploaded and verified.
Would it be the same for addon which is side-loaded, and originally was installed as a part of bundle directly by user?
For side loaded addons, it depends. If you side laoded an addon that was "listed" then yes. If you side loaded an addon that was "unlisted", then it will check your "updateURL" parameter, and if that location updates, then it will update.