Unless you go surfing its unlikely anything will happen.
What mixture and the other admins are concerned about is that the machine will sit there and turn into basically a tool for various types to do harm on there corporate networks.
There is a strong possibility that it will sit there and visually there will be nothing amiss. Just at certain points it might slow a bit as it launches a heap of crap onto the internet. 10-20 machines won't do much. But what the guys are worried about is when 6-7 figure numbers of machines get involved at a synchronised time point. The only way sometimes they can deal with it by pulling the plug to the outside world until it goes away. So what you might say but taking out say amazon for even 30mins is a huge lose of sales.