Ah, I see. Then yes, as long as you are using 2 separate connections then nothing needs to be unplugged.
However, a better option would be to order a faster cable connection and connect both PC's to it using a 2 or more port router or hub. This way it will cost you less per month than 2 separate broadband connections and if only one of you is using the internet at any time then you get a double quick internet connection!!
That is of course assuming that you do not have a good reason for wanting 2 separate connections.