scan can run if the user is logged off but not powered down for this select the option "scan even if user is logged off "
for firing the scan at exactly same time next day :- youcan't do it the scan automatically starts as soon as the pc is powered on and the user logs on to it.
One thing you can do is try to minimize the retry interval time to minimum which may do the job for you. as the scan will try to fire within that time and if pc is still off in that time then scan will start on next scheduled day.