Does the DC-3 have a prop sync?
Judging from this video, it does not have an automatic prop sync. When throttles are advanced you can hear the harmonic beat of the twin propeller blades, and during the climb the instructor seems to manually set the levers to reduce the harmonic set the correct manifold pressure. He may or may not have an indicator to help him, but judging from the sound effects there is no automatic synching taking place.

And here is an old C-47 cockpit procedure training film, on how to fly the aircraft. Nothing on synchronising the propellers.

That beautiful engine sound is not produced by a turbine by the way.