The server could reply true or false if connected or not.
Also reply the SSID, and even the IP address.
If there is more info that would be useful for the technicians in the field that isn't listed above feel free to add.
WiFi connection
Connected:true or false
SSID: "example name"
IP: 129.129.0.23
Signal strength
Pi model
Treehouse image
Software version
Hardware Version