For me scheduled scans seems to occur based on the following precedence:
- Current system status (on/off)
- System load at the time the scheduled scan meant to occur.
- Time of scheduled scan.
Therefore, if system load is above a certain system load limit, the scan is postponed (perhaps for a fixed time duration and also the system load at that next timing).
Note:If a scan fails to occur within a particular day, the scan is skipped altogether till the next scheduled scan (this at least is the way it happens for me consistently).
I think that a good feature to add would be an optional popup which is unchecked by default, to notify more advanced users who want to know that Avast! missed the previous scheduled scan. 
P.S. I am not too sure what happens if the system is off when a scheduled scan is meant to occur.