(Darren) That's correct. The whole instrument would be flat and it wouldn't sound wrong but any other instrument accompanying it would have to tune down a bit. Rather difficult with a piano. One way round it would be to have a small bleed of a lighter gas into the air the organ uses. You could use hydrogen, helium, neon, methane, ammonia or hydrogen fluoride. Perhaps I should patent this lunacy.
Wouldn't some of those risk producing the Amazing Exploding Organ? That puts me in mind of the Large Hot Pipe Organ which produces sound by exploding a propane/air mix in its pipes.
(Darren) It's blown itself to pieces and taken the website with it. I drew a blank with your link, alas. Helium would be safe enough and it's much cheaper than it used to be. It would be amusing to use sulphur hexafluoride, totally inert and non-toxic. It would lower the pitch by over an octave. I think I'd better shut up now.