It is quite possible to get some props out there to go faster than Mach .7, so the optimal RPM would be below redline.
Your tax dollars at work: here's what happens when you speed the prop way over Mach 1. the highlights are mine... -Skip
(found by googling "Thunderscreech")
A project which hoped to produce the fastest propeller-driven plane resulted in the Republic XF-84H, aka the Thunderscreech. The intent behind this project was to take a jet-propelled airframe known to be capable of supersonic flight (that is, a late-model turbojet-powered F-84) and modify it for use with a turboprop engine. This would give a high-speed plane with propeller acceleration and endurance. Note that there was never actually any intent for it to reach supersonic speeds, though that claim appears in many references.
The test flights proved that it was a fast (though it never flew over 720 kph, due to handling problems) and quick-accelerating aircraft, among the fastest prop jobs of its day. It also, however, held another record, one hinted at by its nickname. It was arguably the loudest fighter plane ever built. The howl of the 6000 shaft horsepower (and that's without the afterburner) twin-turbine engine combined with the
roar of the prop made standard ear protectors irrelevant. Worse, during, run-ups the blade tips went faster than sound, reaching Mach 1.18 (it was a constant-speed prop, with thrust adjusted by changing the blade pitch). This produced
multiple sonic booms which could pummel ground crew members insensible in short order. Due to prop torque the plane was a major handful to fly at high speed. And, as with any experimental plane, it had development problems. One pilot reported that 10 of his 11 flights were cut short by emergencies of varying degrees. Another made one flight and refused to get back in the cockpit. The plane - two were built, one of which survives - deserves an article all to itself, or perhaps extensive mention in an "it seemed like a good idea at the time" article. Among other claims to fame, it was the only turboprop aircraft to have an afterburner. (This was never lit in flight, probably to the benefit of the pilots.)