I've never lived on a narrow boat, but my understanding is that it would depend on the administrators of your moorings and the relaxewd approach of the GPO. Don't see why not.
In the Valuation office Guidance for liability for Council Tax, posted elsewhere on these boards, having post delivered directly to your boat is one of the tests used. Ie if you get post delivered then you are almost certainly liable. However, if you never go anywhere, and they know it, you're liable anyway!