iCal does not need to be running, once your Alarms have been set up !
Your Mac however does need to be 'on' or 'awake' it will not wake it from sleep !
So if you want your Mac to 'wake' or 'startup' at a specific time...
just go to the System Preferences-->Energy Saver-->Schedule
and set when you want your Mac to start up...set this to 5 minutes befor the first iCal Alarm is due to run...
...then your Mac will be ready for action !
regards
Ric