My question is: Will the scheduled automatic shutdown not work if the computer is in sleep mode at the scheduled time of shutdown?

I have energy saver running and both iMacs I work with are scheduled to start at 9:45 a.m. and shutdown at 8:15 p.m. However; when I show up to work in the morning the iMacs aren't actually booting up at 9:45. They do show the display at that time but it acts as if it is coming out of sleep mode because if I need on the iMac before 9:45 a.m. I only have to push any keyboard button to turn it back on.

These iMacs are not connected to each other in any way. (Other than being really cool machines.)

I work in a library and both iMacs have Faronics' Deep Freeze because they are used by teenagers and we don't want the settings messed with. Because of this, I really need these iMacs to shutdown completely in order to reboot to the proper settings and I'd like it done automatically.

Any information would be greatly appreciated.