it sure will. I have a similiar set up at home. I have ntl internet connection plugged into router this router is plugged into Apple airport which tranmits internet around my house.
I connect wireless to the internet through both my laptop and pc with wireless cards (laptop is built in and pc has an external card)
works perfect well since i set it up. although make sure you make your connection secure so others can't piggy back.
can't see why it would not work with any other wireless router be it linkys or apple airport