Now that's a hacker idea if I ever heard one. I assume the way to do it would be to use a modem the same way the internet operated over dial-up. Listening to the vinyl would sound the same as when you accidentally picked up a phone on the same line, a static-y kind of squeal.
It does make me wonder what the maximum practical bitrate would be -- more than phone lines with their severely limited frequency range, that's for sure. Could it handle CD-quality FLAC audio?
It also makes me wonder how you'd manage records wearing out. What type of distortion occurs, and how might that affect how you'd spread bits over the spectrum, or would it affect which error correction code you'd use?
I doubt it, since CD-quality audio is already objectively better (for human hearing) than analog audio on LPs. The only thing LPs are better at, sound quality wise, is extension into the ultrasonic range of 20-30+ kHz (which we can't hear anyway) but the SNR and distortion metrics are much worse in the ultrasonic band than the audible range.
I'm not sure if this is a named principle, but it seems intuitively obvious to me that on any particular encoding medium (magnetic tape, vinyl groove, etc.), you can encode "more" data in an analog way than digital, since with digital encoding you need to be able to make distinct symbols onto the medium, and represent any signal fluctuation with a series of such symbols; whereas with analog encoding a tiny fluctuation in what's recorded to the medium can correspond to a tiny fluctuation in the signal. Of course the tradeoff is that digital data is much more immune to distortion from imperfections in the medium.
If the same track width and pit sizes on CDs were used to encode audio in an analog way like LaserDisc does video (the continuous distance between pits being modulated by the signal), no doubt it could encode well into the ultrasonic range and surround audio channels via modulating them into different frequency bands. But it would have its own characteristic "surface noise" and "pops and clicks" just like vinyl.
It doesn't seem obvious to me, because I'm not talking about encoding distinct symbols into the medium. I'm talking about using the entire available frequency range to encode digital information the way a modem does. And I'm talking about using lossless compression as well. And as you say, if an LP can encode ultrasonic information, that opens up all sorts of extra space for information that is useless in analog.
It may very well be the case that an LP couldn't record CD-quality audio, but I do very much wonder what kind of bitrate would actually be achievable. A dial-up modem is 56 kbps, using the frequency range 300 hZ to 3.3 kHz. CD audio is 1,411 kbps, but vinyl frequency range is from 7 hZ to 50 kHz, which is 16x wider than a dial-up modem. And you can pack much more data into higher frequencies.
So on the face of it, digital CD-quality audio seems like it might be very much achievable in theory on vinyl. But again, when you account for error correction and degradation and particularly distortion, I wonder if you could actually get it reliably in practice.
What's next, encoding a ZIP file onto a wax cylinder?