Theoretically, yes Dawger is correct.
However, I'm almost POSITIVE that there is a mechanism that can allow the prop RPM top exceed the engine RPM so that it doesn't over-rev itself (unlike the WW1 planes that are very easy to blow the engine on in a dive for this exact reason). Because of this, I'm not convinced that an increased RPM due to being in a dive really has anything to do with the engine's RPM.
Also there are design differences between carbed and injected systems. I know we're not talking about electronic injection here, but maybe the mechanical injection systems of the day had ways of preventing fuel flow during such maneuvers?
I do know that in the old days, one way to increase fuel economy in a car was to hold the clutch down while going downhill, this way the engine would idle instead of rev during these times... but on electronic fuel injected cars the opposite it true. With your foot off the throttle and engine RPM staying high, it can actually cut all fuel flow at the injectors (or at least below the amount it would use at idle) which means that even at 3000 rpm, it is possible for today's cars to get better fuel economy going down a hill than at idle. Whether or not this has any relation at all to WWII aircraft is beyond me.