So, you have the red exclamation point icon on your desktop that warns you that you haven't got all the latest updates. On my FC3 box, where I don't have any access to the RHN (Red Hat Network) for updates, I instead get a gray icon with a question mark, indicating that the an error occurred when the system tried to contact RHN.
If you click with the right mouse button on it, you can exit that warning system.
How you can stop it from being started when you login, is probably a different story.
But that wasn't what you were looking for.
If you disabled internet altogether, I suppose you should get the error message that you can't reach RHN too.
So I'm guessing your internet may not be disabled entirely.
Could you please try "netstat" to see if any of your ports are still open? And can you tell us how you disabled your internet connection?
Did you disable the network card altogether? Or did you disable some (but perhaps not all) network services?