As noted by Mattias Nordqvist in the comments below, you can also select the radio button option “Run whether user is logged on or not”. When saving the task, you will be prompted once for the user password. bambams noted that this wouldn’t grant System permissions to the process, and also seems to hide the command window.
It’s not an obvious solution, but to make a Scheduled Task run in the background, change the User running the task to “SYSTEM“, and nothing will appear on your screen.
