I don't know about OS9, or indeed about using a dial-up modem, but under OSX, with the machine connecting to the Internet through the ethernet connection, I have never experienced any problems. In fact OSX really works best on a connected machine as software updates etc come down automatically.
Under OSX you can have things like e-mail, and web browsers open in the background. You can even browse etc whilst Media 100 is rendering or exporting in the background(something I believe you couldn't do before). The only thing Media 100 can't do is digitise in the background - as soon as you switch applications, media 100 stops.