Can I turn off my computer while Minecraft is downloading

No. It's impossible for the computer to finish downloading if it is off.

Nope

Of course you can power it down, however, it will pause the download until you resume it. You can't power your computer down, and still expect a program to continue downloading. This is because data can't be written to your hard drive (this is where a download's target is) while there's no power going to your computer.