Solution: 120°

The answer is no.

The minute hand travels 12 times faster than the hour hand. The first time it is 120° ahead of the hour hand comes from solving

x + 120 = 12x
where x is the progress of the hour hand, measured in degrees. x=10.90°, which is 12:21:49.90 AM. The second hand is not in the right place, however, nor is it the first time the minute hand is 240° ahead of the hour hand.

By solving these equations 11 more times, offsetting the the hour hand by 30° each time, we see the second hand is never in the right place.