I think you will find that with all Android smartphones, the phone has to be switched on as the alarm clock is just an app like any other that runs on top of the operating system. You can no more process a video in Windows while your PC is turned off than you can have your alarm clock sound an alarm on an Android phone when it is switched off.
Nokia uses a different system. The alarm clock is in hardware and can hence turn the phone on or sound an alarm even if the phone is off. However, you can't replace the alarm clock on Nokias, unlike the hundreds that are available on Android.
If you are concerned about it disturbing you with calls / emails / texts while asleep then simply put it on silent when you go to bed and plug it in, or use one of the hundreds of apps that can do this automatically. The alarm will come on just fine when its time for it to go off.
Leaving your phone on overnight has a number of advantages. Your alarm will work. Your phone will log all missed calls and messages that occur while you're asleep, and all your emails will be sat there waiting for you.
You can adjust all of the volumes individually (Ring, Alarm, Notification, Media, System, etc), but the silent mode does NOT silence the alarm - it only silences the Ringtones and Notification tones. Also when you set the alarm itself there are a bunch of options to set volume for that specific alarm.
None of the other alarm apps will switch the phone on, but if you want to have a look at what is out there search the Android Market