No, the OP sounds like he literally wants to use the voice "line" to dial-up to his current dial-up internet provider that he is already paying for, and use the internet that way instead of paying for a data plan.
No. Can't be done, even from a theoretical standpoint. Analog dial-up modems assume a clean, analog line with certain acoustic characteristics. Way back in the day, when cellular phone calls were analog FM transmissions, you could get hookups for your laptop's modem that would allow it to dial-through a cellular modem, but even then it was very sketchy and unreliable.
Today, nearly all cell phones use digitized & packetized voice channels (which, on account of jitter, will completely throw off the timing of the analog modems on both ends), and on top of that, the audio stream is run through a lossy audio compression codec that is specifically tuned for the human voice (which will totally screw with the modulation, causing both modems to sound like unintelligible garbage to the opposite one). There is absolutely no way that a dial-up "waveform" would survive such an environment.
-- Nathan