Yep, that is how I would do it. I am sure that it's just a simple voltage recieved by the tach that tells the needle where to go. When you hit the voltage equal to 3000 rpm, you could activate a relay. The problem is that the cutout's work on a momentary switch and using this method, you'd be driving the motor for the full duration of time above 3000 rpm. Then when you transition below 3000, all it would do is remove the drive signal from the cutout motor. That would not close the cutout, but just leave it in the open position.
Honestly the way to make this work is a circuit like I mentioned with a simple relay, but instead of a motor-driven cutout valve, you need a normally-closed non-latching solenoid. It would open fully in an instant, and would stay open as long as you were above 3000. Then it would instantly close as soon as you got below 3000 and the excitation voltage from your relay ceased. Unfortunately I have no idea if anyone actually makes a cutout like this. I'm sure you could find an industrial valve that is solenoid operated like this but the cost is an unknown to me. And probably not cheap.