Do quadcopter propellers break the sound barrier?
Almost certainly not. Given the comments specifying a $0.5$ inch radius (blade length,) that means the circumference of the path of the blade tips would then be 

$$2 \pi \cdot 0.5 \, \text{inches} \approx 3.1415 \, \text{inches} \approx 0.2618 \,\text{feet}$$

To get to the speed of sound (which is approximately $1,126 \,\frac{\text{ft}}{\text{s}}$ at sea level,) that means you'd need to have the fan spinning at 

$$\frac{1,126}{0.2618} \approx 4,301 \,\text{Hz} \approx 258,060 \,\text{rpm}$$ 

Needless to say, that's not happening unless you have one seriously expensive quadcopter.

The buzzing you hear is probably either the frequency at which the motor is spinning or, perhaps, the frequency of some oscillation of the fan blades. Most likely, though, it's just the frequency of the motor/fan.