Set up the Tune-up schedule for the frequency and time that you wish in OneCare.
Configure a task in Windows Scheduled Task that will wake your computer from Sleep to occur shortly before that time and set your power settings to put the PC to sleep again after x minutes of inactivity. The task can be as simple as opening Notepad.
Note that you cannot turn the PC *off* to have this work, it needs to be suspended or in sleep state.
Your screensaver and hibernation cannot be configured with that level of granularity. They are on or off and jump into action based on "inactivity" - meaning your use of the PC: keyboard/mouse/other input. OneCare running won't stop a screensaver from honoring the timer for countdown, nor will sleep/hibernation be stopped if OneCare is running a task, so you'll need to set the time to suspend to be at least as long as a typical tune-up.
-steve