Unless there is a timer on it, a button to be pushed by a pet or a power surge to speak of. Then sure why not, could be possible I suppose.
Same thing happenned with me also. My radio turned on by itself, it was close to midnight. My radio does not have alarm on it. This is the First time it happenned.
It could be a poltergeist or it could just be that your alarm is set to "radio" but I would says it is just the radio. If it was happening with lights or the TV or other electrical things then it might be haunted. You can always tell the ghost to stop if you think it is a ghost.
Not necessarily. Perhaps the alarm is set to "radio"