VOIP systems run a lot like the old Sprint PC Pursuit, they are packets
as you said. A driver could be written to allow for this as was done
for OGG-Net.
Unfortunately, most VoIP systems don't work that way. With standard
VoIP, the audio that the modems send is digitized and the digital
audio stream is sent over the internet as audio. Protocols like V.150,
on the other hand, work almost exactly the way PC Pursuit did. The
local V.150 VoIP gateway acts as a modem and converts the audio your
modem sends back into the original data stream. It then sends the data
(text, files, whatever) over the Internet to the remove V.150 VoIP
gateway which, having received the data without error, acts as a modem
by converting the data back into modulated audio into the distant
modem.
Systems like this are said to work perfectly but, unfortunately, I
have never found a VoIP carrier that supports these protocols.
As you say, it would be possible to implement this type of technology
on both ends but if I were going to run a BBS, I'd prefer that people
could just dial it directly without having to purchase and configure
exotic hardware on their end :).
-Rusty