In theory you can run anything over this that could run over a long distance PSTN link.
In practice most modem technologies do not handle jitter and packet loss well at all, and quirks which a human would not even notice will trip up a data call. It still works, I have clients running credit card machines on VoIP lines all day, but the longer the call and the higher the bandwidth the more likely something is to go wrong. A short 9600bps data exchange from a card machine is a lot easier than a 30 page 33.6k fax which is a lot easier than a 56k modem on a PC.
There's a special method called T.38 that allows VoIP providers with compatible endpoints to convert digital fax calls back to a data stream instead of audio which makes it a lot more tolerant of delay and jitter as well as slightly more tolerant of loss. Something similar could hypothetically be done for data modems but I haven't seen it.
G.722 might sound better to humans, but G.711 is definitely better for modems since it’s effectively just uncompressed PCM (disregarding a bit of dynamic range compression which modems are generally fine with).
It would be possible to mask this with a relatively simple FXS device to hide all of this and pretend it's a modem while packetising the actual data, but I guess the demand is almost zero so why bother.
I've been looking for a solution for many years to retain dialin services without having racks full of modems and trunks that are rapidly going out of fashion and at some point will not be available except via IP (and now we have the same problem at both ends), but they just don't exist.
Regular modems can't make use of that, since the actual phone lines they were designed for (whether analog or digital via G.711) didn't support more than 300-3400 kHz anyway, so anything beyond 8 kHz sampling (corresponding to a Nyquist frequency of 4 kHz) is wasted on them.
Maybe you could go crazy with a custom modem that knows how to exploit the additional high-frequency components of G.722 while dealing with the lossy/psychoacoustic compression across all bands, but I doubt it would yield any improvement over G.711:
> It is compressed, yes, but at higher bitrates it is actually usable for modems/faxes
No, they're both exactly 64 kbps (after compression/"compression"), so you wouldn't be able to fit any more signal in it from an information theoretical point of view.
I had a project using hylafax with about a dozen USB fax modems hooked up to a SIP gateway, connecting through a VPN back to the office where the PBX was and then out to our SIP trunk provider on G.711. It sent a lot of 2-10 page faxes. The system sent over a million faxes over its life, and excluding one receiver that tended to constantly have problems no matter what had an >95% success rate.