Can I install games from Steam while my computer is off?

You can't. If you want to save energy, just turn off your LCD.

Don't wait until the download is complete, just do your daily life as usual and let your PC do it`s job.

You can't install it if your computer is off, but you can download them in the background while you play other games on Steam.

Go to Steam>Settings>Downloads and check Allow downloads during gameplay.

Here are some pictures to guide you.

I hope this helps you.