Yes. Especially if that incumbent governor is finishing his second term, which is where Jindal is at. He'll leave office January 2016, as the Presidential race heats up. If he's succeeded by Republican David Vitter, he can run for President with a feather in his cap.
So yes it's doable.
But then he wouldn't be an incumbent. Still, as you point out, if they have done a reasonably good job, second term governors from those states can ride the momentum from having been recently in office into the campaigning for the next one, be it the Presidency or a Senate seat.
