Would a headwind result in a faster propeller rpm?
The problem is you're holding the aircraft with your hand.

Imagine a windmill. It has no power at all, it spins freely. What happens when wind is blowing at it? It turns.

Now imagine a propeller with no power connected to it, so it acts like a windmill. If wind is blowing at it, it will turn just the same. Why? Because a propeller pushes wind backward when it turns. When it is facing a headwind, the propeller wants to turn such that it is pushing air at the same speed as the arriving air.

In your case, I suppose the fan is blowing air at a faster speed, compared to the propeller is pushing air on its motor. Say the motor pushes air backward at 1 m/s. The fan blows air at 2 m/s. That's why it spins faster with the fan on.



But that's only true as long as you're holding the aircraft with your hand.

In flight, nothing is holding the aircraft at a constant ground speed. For example, assume in a no wind condition, an aircraft is flying at 80 knots. Suddenly it encounters a 10 knots headwind, and continues to fly into this headwind for the remainder of the flight. What happens?

At the moment of encountering the headwind, the airspeed indicator in the cockpit jumps from 80 to 90. The propeller rpm will also suddenly jump to a higher value. But that is not going to last. The aircraft is getting pushed backward by the wind, the airspeed is going to slowly drop back to 80. There is not enough power to keep the propeller at the higher rpm which pushes air at 90, it can only to 80. After a while, it is flying at 80 knots relative to the air, and 70 knots relative to the ground.