In most cases, yes your screen will automatically switch off because it will be inactive after it finishes. For example, most phones are set to automatically sleep when not in use for 10 minutes or so.
On a TV you might need to set it to switch off with the in-built timer. There is always a way to get your screen turned off after a quick Google search. You can use this video on so many different types of screen that there is too many to cover here e.g. phones, iPads, tablets, TVs, PCs, laptops, MacBooks, monitors.