Traditionally LOA was measured from the point that the line of the deck met the line of the stem to the point that the line of the transom met the deck. With reversed transoms, this convention eventually was altered to the length of hull from the stem to the furthest aft point on the transom. An outboard rudder would not extend the LOA any more than it would the waterline length.
That said, today, you see ads and the like that include all kinds of corruptions of traditional definitions. You see LOA''s that include the length of bowsprits and boomkins, davits and any other projection fore and aft. In my book that is just plain disingenuous and shows a lack of honesty on the part of the advertisers.