Yes and no. An alternative is to use a Raspberry Pi instead of a laptop. This can be pre-programmed and ready to plug into the screen. If you do wish to use a laptop then yes, the laptop must stay connected to the screen, have internet access and stay switched on. If the laptop switches to sleep mode (or screen-saver) then the second screen will automatically go blank. It’s the same principal as using a projector for a slide-show.