Monitors aren't used by the VIP, but by the pool (or the node, but I would limit those to very simple checks).
In this case, the pool would use the monitor to check the health of the pool members. If you were to use the monitor I included above you'd simply be making an HTTP request (TCP, port 80). However, as that monitor would make a single external site a dependency for all your internet requests from internal clients I would be hesitant to use it. You could mitigate this dependency to a degree by creating multiple monitors (accessing different properties on the internet) and requiring only one check to pass.
Have you been able to determine if the Bluecoat boxes can tell you whether they have connectivity to the Internet?