As a former Time-Warner Technical Support employee, I will have to say no, this can't be done with just the eMTA (that's the phone modem.) It is possible to get this working with additional hardware/software that others have suggested, but beware - Time-Warner will not troubleshoot this connection, since it is not an ordinary phone jack and therefor beyond their scope of work. If you had any problems getting this to work, or keeping it working.....the only place you could go for help is a forum - assuming others have tried this and succeeded.
Also, in our division at least, the service goes out A LOT. It is not the most reliable to say the least ... You'd be amazed at how much we, as a culture, have come to assume that when you pick up the phone there will always be a dialtone. If you have gotten Digital Phone, please leave that notion at the door ... and try not to get too frustrated with Tech Support -- they're there to help ... If the service goes out too much for you to handle, then cancel it. No harm, no foul.
I know it sounds unrelated, but I am trying to do something similar but without phone service at all. I want to hook my computer, cell phone, and house phone (which has no dialtone) all to run off of Bluetooth technology, but I'm running into a lot of road blocks.
Phreaking just isn't as easy as it used to be.
~Jax