It's more of a hardware issue than anything else.

The Wii can only receive from the Internet in one of two ways:

1) It's built-in 802.11 Wifi
2) The Ethernet port in the back.

Neither of these formats are dial-up compliant out of the box. You would need to enable ICS on a PC with the dial-up modem and then share out the signal to a router/Ethernet card to be able to transmit data to the Wii.

Although, I suppose the whole process could be simplified by purchasing the Nintendo Wifi dongle and just transmitting straight out of your computer that way.