Summary to my last post:
When your ears are close to a melodica, the position of the melodica makes a big difference in the way it sounds to you (or a mic). Tubes, mouthpieces, and no mouthpieces do not change the sound of the melodica as much as we think. They change the angle and distances at which we listen to the melodica, hence they appear to change the timbre.
Ears far away from the melodica do not hear the positional differences of the melodica. Far away ears hear an average of the timbres and the very powerful influence of room acoustics. Hence, I hypothesize that tubes and mouthpieces do not appreciably change the timbre of a melodica. Playability perhaps, but not timbre.
Does that make sense to others? It is still a hypothesis, but I am willing to bet beers on it.