Look at the backplate with the faceplate off. There are two LEDs on the PCB, a green LED, and a red LED. If the green LED is off then the thermostat is not communicating with the WiFi network. If the green LED is blinking then the thermostat is in ad hoc mode and is ready to be put on your local network. If the green LED is solid then the thermostat is on the network and communicates.
Another way to see if your thermostat is communicating with the network without taking the faceplate off is to look at the LCD display. For newer backlight versions, the display will show a radio tower if the thermostat is in ad hoc mode, signal bars if the thermostat is on your network, and if there is neither the thermostat is not connected to a network and not in ad hoc mode. The signal bars do not indicate signal strength, only that there is a signal being detected. On older generation non-backlight thermostats, the display will show a satellite icon if the thermostat is in ad hoc mode, satellite+lightning bolt icons if the thermostat is on your network, and if there is neither the thermostat is not connected to a network and not in ad hoc mode.