Hi Andy,
This is the project i was referring to - it uses an Arduino with an Ethernet Shield to push an HTTP request to PushingBox that can then carry out a set of actions you configure. In this example, the guy also has a networked webcam exposed to the internet via his router and when the doorbell is pushed, he gets emailed a photo by PushingBox from that camera.
I have successfully managed to get PushingBox working with Pushover.net (its about as easy as it gets!) to give instant push to my phone... not tried the doorbell thing yet though.
although he is using an ethernet shield, i don't see any reason it wouldn't work from your Yún - but I would be mindful of the possible faraday cage effect of a metal post box on your WiFi signal!
James.