I got my first Android handset. My previous Nokia Smartphone the alarm would turn on even if you turned the phone off then it would ask if you want to turn the phone on. I have tried it on my LG E975 and it doesn't seem to work all but just once it worked when I set the alarm 2min away and it turned on but not when any longer ...
Does the alarm not come on when the phone is off? Running ICS I think.
I think the basis of Smartphone OS these days is that, if the OS isn't booted up and the phone doesn't stay on stand-by - e.g. the phone is completely powered down: off - then nothing is operating. Which in then, the alarm app isn't triggered by the quartz clock.
Symbian has different approach to the way how alarm works.
I use an app called profile scheduler, make a few nokia style profiles then tell it when to turn a few things on and off. Ie turn cell radio off at night, or notifications or however you want it (except off) .
It also has a useful addition that it can look in your diary and go silent in meetings too.