I have always thought that the android phones are unable to turn on when the alarms are triggered is a bug.
In fact, my old Nokia n810 (an internet tablet) is able to turn on with the alarm, even if I take the battery off and put it on again (of course, with no battery It doesn't turn on, but what I want to make clear is that It is completely off). It is buggy (the tablet tends to freeze when it is in process of turning on, so it is difficult to press the off button which doesn't responds properly), but it does turn on.
I like to turn the phone off at night so I can charge it while I'm sleeping.
Ohh, and I arrived this post looking for an application that do just that.
I guess I would need to keep relaying on my good old Samsung E1205 which turns on without any problems.