It might let you play for a while, but I'm going to guess sooner or later Warden is going to interpret it as malicious. Either way, the game takes up less than 1 GB. However, do remember you need to install the full version of the game, not just Multiplayer-supporting-version in order to play without a CD. You could risk it if you want; from what I remember, Battle.net itself only cares about the CD Key.

So what exactly is wrong with your regular computer? That'd explain why you haven't been on since we started.