That depends on the CODEC used. Cell phone CODECs, designed to minimize bandwidth are strictly voice only. However, the G.711 CODEC, as often used for VoIP, is the exact same CODEC used for the full 64 Kb digital voice channel. As I mentioned, I have set up FAX over VoIP. That said, there may be issues with using it over the public Internet, due to latency etc..
BTW, you're talking to someone who's worked in the telecom industry for many, many years and first came across digital voice carriers in 1975.
I haven't lost my mind. It's around here...somewhere...