That can't happen. If the device is OFF, its off. Period. No calls, no messages, nothing. The charge led can be on to indicate charge /full and you may get a battery icon on screen when charging but if the device is really off, it's dead.
When your phone is charging, the LED blinks red to let you know it is not fully charged yet. It will do this when the phone is off and when the phone is one but at the lock screen.
When the phone is on and not at the lock screen, the LED will not flash red while it is charging so that other apps can use the LED.