Here is a way to do it but it will waste a lot of battery power if you don't have an Amoled screen:
- Install No Screen Off. This allows you to always keep the display on (although it doesnt look like its on since it will be on a black wallpaper).
- Install Draw on Screen. This will allow you to draw on any surface on the display.
- Open Draw on screen and get used to the controls so you know how to use it.
- Download a black wallpaper and open it using your photos app in immersive mode.
Now you should be able to draw on the black screen as if the phone was turned off. Considering you have an amoled display, this won't waste much battery. If you ever want to go back to the normal screen, simply tap "shut down" on the top of Draw on Screen and go back to the homescreen.
For more reference to how to use Drawonscreen, check this link: How to draw on any screen on android device