If you lean left, front wheel will "do" countersteering itself (same as noted). Since gyroscopic effect on bike is not so big and speed, mass is not bigger than rider it is not noticable. For motorbike you cannot just lean hence need for explicit countersteering because of much higher forces involved.
So I think it is correct to say that countersteering is always required.
So I think it is correct to say that countersteering is always required.