Time Warner "Digital Phone" still uses an analog line emulator in the box on the premises. That way, standard house phones will work. This should not destroy the unit.
However, the Tieline probably will not work well (if at all) on a VoIP line. The Tieline has a modem in it that's similar to a computer, and the speech codecs that are typically used on VoIP do not pass modem calls or fax data very well, if at all. You need a real POTS line to make a POTS codec work properly.
If the location has Time Warner VoIP, maybe they have a high speed data connection available too. If that's the case, then an IP codec like an Access could be used. If you have a Commander G3, I think it has IP capability. A laptop with IP codec software could also be used.