Can i use my laptop being off as a monitor screen?

Hi so i was wondering i have a laptop right, and i want to know if my alienware alpha "console/pc" will it work if i connect it via HDMI to my laptop?

Does this mean the data wil go to the laptop, or will the laptop be turned off,

and it will use my alienware alpha as the main PC and the laptop screen the screen for it?

Can i use my laptop being off as a monitor screen?