I don't think it's possible with android. Since the phone is off, the processor would not be able to trigger the alarm. I've heard of other phones that can do that, but with android, it's completely off.
Yeah, I'm not either way. As Jeremiah said, some phones can do that. My girlfriends old SE for example, but that doesn't run Android. I would likely side with Jeremiah and say that once the OS has been turned off, any alarm app will not be able to function.