Not all of my reboots occur when the screen is locked. And without the screen lock, I would have to worry about the phone turning on when in my pocket, etc...
Mine would reboot at random too. I just tried the app. Worked for me. It will be a bit hard for it to turn on. Still have to push the home button to turn on.
Check again. I tried No Lock, and *any* of the buttons on the phone will turn the screen on, not just the Home button. This includes the camera button, the volume, etc...