It seems obvious they probably don't exist and it's hardly possible to prove they do. But if they did (proving they don't exist seems equally impossible to me), I could only imagine they would communicate the way I describe.
Nevertheless it indeed seems a curious exercise to invent a framework for meaningful communication to be logically possible over a channel of such a nature keeping its fuzziness in mind.
I instinctively try to make the least bald assumption possible. Of course, as we exercise unconstrained imagination, we could imagine a ghost being so mighty it would materialize beautiful LaTeX documents right on our hard drives manipulating magnetic particles on them. Nevertheless, if I forget about the doubt in ghosts existing at all for sake of fun or whatever, the next doubt I have is they can manipulate the matters of material world with ease and precision - even if they could manifest a blow of a wind it would probably be hard for them to manipulate it precisely enough to produce continuous ineligible speech.
Nevertheless it indeed seems a curious exercise to invent a framework for meaningful communication to be logically possible over a channel of such a nature keeping its fuzziness in mind.