It's worth a try. I know fax machines work with Cox home phone(VOIP) and I can't imagine a dial up modem would be much different. Just set it to a low speed like 28 or 33Kb and turn off error correction.
dial up modems will work just fine. Digital phone service means it's digital to the device that converts it to analog signal for telephone service. You can use a fax or dial up modem without issue. I have a U.S. Robotics Dual Standard HST connected running A.C.I.D. (Audio Caller ID), it announces all calls I receive through my computer speakers. Works just fine.