What I should have said..... that the heat in the extracted air, with it's moisture burden, will be lost into the huge cold space of a stack, and get dumped. If you were not careful it would end up like the garbage compactor in Star Wars; dianogas jumping all over the place!Venting into the stack will leave you with a damp (and possibly greasy & smelly) stack. The stack will not warm up enough along it's full height and the moisture from cooking will condense in it.
Well, nearly.