I don't think it's practical. The lossy compression that GSM uses is incompatible with the protocol used with modems, which assume the analog characteristics of real phone lines.
If you want to reach a BBS on your phone, you could use a telnet app like Termius or Termux over 4G.
There's certainly practical issues, but not every call is stuck with the GSM codec anymore. G.722.2 (aka HD Voice) may be better than GSM at carrying modem noises (or it may not be).
Of course, way back when, when mobile carriers had modem banks for outgoing calls, that worked a whole lot better.
Fax connections over GSM required a special (read: expensive and inefficient) circuit-switched data service that was limited to 9600 bps, at least here in the U.S.A.:
Same in Europe, HSCSD and all. Though at the time, I thought my Nokia 6150 was really "modem'ing" and the 9.6kbps were because GSM compression and available bandwidth would obliterate anything else, but nice to learn after all these years that it was actually digital and the endpoint with the actual modem was somewhere in the network.
The way this would work is that your cellphone would send the fax data over the digital cellular network connection; in turn, the actual cellular network itself would speak the V.29 fax protocol.
Take a look at the Quiet Modem [1] project, which has bindings for Android and iOS if you're looking for a softmodem. I'll bet there's telnet apps on iOS though if you just want to do some IP based BBSing.
I remember someone trying to port minimodem to run under termux. Nevertheless, it still not a HAYES modem, but I don't think it is difficult to build one using minimodem.
If you want to reach a BBS on your phone, you could use a telnet app like Termius or Termux over 4G.