I'm in the Steve Gardham school of thought. The Melodeon and Concertina are fragile and made of materials that are susceptible to damp, so their life would surely be short at sea, and particularly so in wooden ships.
No doubt they have been there, but I'd consider it unlikely that someone who'd paid good money for a good instrument would expose it to the conditions of the forecastle.

All free-reed instruments are of comparatively recent invention anyway, so there aren't enough years for them to have a long history.