Can Xiaomi switch on and off the control light when he is not connected to the Internet?

You can't. Xiaomi intelligent switch is used with gateway and needs to be controlled in the local area network. It is impossible to control lamps without networking. Xiaomi Mijia's screen display switch has two different buttons: single billing control and double opening single control. Intelligent scenes such as remote switching lights, voice control switching lights and turning on lights at home can be realized without changing the wiring of lamps.