If we take a single seater electric gyrocopter like this one, could a human-powered propeller like this add to the endurance of the aircraft? The gyrocopter only needs a 32km/h forward speed to stay airborne.
According to the wikipedia page on "Human Power", a trained cyclist can produce about 400 watts of mechanical power for an hour or more, adults of good average fitness can produce between 50-150 watts for an hour of vigorous exercise, and a healthy laborer over the course of 8-hour shift can sustain about 75 watts per hour.
The Electric motor on the autogyro mentioned in the question has an 80kW (i.e. 80,000 Watt) motor. However, as you know most aircraft only use 100% power on takeoff and approximately 75% for fast cruise. For simplicity, I'll assume 75% power for cruise. That is 80kW * 75% = 65kW (i.e. 65,000 Watts). The information from the AutoGyro says the current endurance is 45 minutes.
So, if we assume the "trained cyclist" power output of 400 Watts, which is 0.62% of 65,000 Watts, then it would result in a 0.62% increase to the current endurance of 45 minutes. A 0.62% increase would result in an increased endurance of approximately 17 seconds of flight (45 min * 0.62% = 45.28 min or 45m 17s).
Its important to note that the human powered glider mentioned in the link was designed from the ground up to be powered by human power. It only weighs a fraction of the electric gyro. For example, a similar human powered glider the MIT Daedalus weighed just 69 lbs (31kg)! (https://en.wikipedia.org/wiki/MIT_Daedalus). The gyrocopter in the question appears to be a modified version of the Cavalon model by the company AutoGyro; on it's technical details page it says its empty weight is between 606-672 lbs (275-305kg).
One has to look at the total energy requirement of the gyrocopter. In this instance it is a 80 kW powerplant. A human power plant would be incapable of a sustained output of more than 1kW, therefore I would conclude that the impact of augmented human sourced power would be less than 1% and therefore insignificant.