Will my antivirus system scan my computer even though my computer is off

No this is not possible because .exe files can't be executed when a computer is not online. <Supv note: 1) "online" in the sense of "powered on and running". The computer would not need to be connected to the internet for the virus scan to run. 2) If you intended to ask "Will my system scan your computer?" You will need to re-post since I am re-wording the question.>