It can if configured (at least on 7.5, 7.6 and 9.0).
Right click the server that's managing the client -> all tasks -> SAV -> Scheduled Scans. Select the Client Scans tab, highlight the defined scan and edit it. Click advanced and it will bring up a window where you can set it to "Handle missed events within X hours of the scheduled time". Since you're running at midnite I would set that to somewhere between 4 and 8 hrs depending on when the users show up to login. If this setting has timed out the user will scan on login.