Boy! There sure are a lot of people that have all the answers in here.

Hey there Cfowler, your question is fine, no further explanation necessary for me. What you are asking is a question of hardware layered protocols. The answer is, as most hastily supply without knowing why, nope, can't really do it that way. I say not really because although the dial-up server, I assume you want to use your cable modem to attach to a dial-up server, based on your original question, you could possibly use another computer, a go between of sorts, to make the connection on your behalf. However if your intention is to use your cable modem to perform as a dial-up modem, you are of course out of luck. However, it is worthy to note that the technologies you query in the sense of cable to coax may be similar to an actual cable modem's potential. What I mean to say is, in your cable modem, you change (lamens) coax ethernet to twisted pair etherenet. It could just as easily have been coax ethernet to regular telephone line. However, that being a possibility, your speed would still be severly limited but now due to the medium.
Wow, it almost seems like some people are really offended by such a question. Pssst... Do they know if the question bothers them to that degree that they are not obligated to respond?
Keep smilin'
Just my opinion, I could be wrong.
Just passing through, caught my eye.