The answer to your question is, "It depends". If you are turning the
computer all the way off, then scheduled tasks and maintenance won't run.
But if you are putting it to sleep (which is what many newer computers do
when you push the power button) it will awaken and perform tasks.
My answer might be too simple: every machine needs to be turned on in order
to do something. Without power on, your computer is not able to operate.
Axel