I'd like to have my webserving arduino update a mobile site when a status variable changes in a program running on the arduino.
Generally speaking, servers do not make connections on their own to other sites. They wait for a client to make a connection request before they do any external communication. That being said, an arduino can both act as a server and client at the same time if needed. The moble site will need to be a server to receive any unrequested data from the arduino.