It is hard to find any detailed information on the active noise cancelling. But from what I could find, it is only supposed to cancel out engine noise; not tire noise, wind noise, mother-in-law noise , or other undesirable noise unless the noise happens to be the same frequency as the engine noise.
Here is the description from the shop manual:
Active Noise Control
Active noise control is an audio system feature that eliminates some of the low frequency engine noise within the passenger compartment typically induced under wide open throttle or heavy part-throttle conditions. The system uses 3 microphones, a DACMC, and the audio system speakers. The DACMC determines the noise frequency to be canceled based upon engine rotation speed data from the PCM and the microphone input signals.
While the engine is running, the active noise control microphones located in the front and rear of the headliner monitor the engine noise resonating in the passenger compartment. The microphones transmit this noise as analog signals to the DACMC, where they are converted into digital signals by the integrated analog/digital converter. The digital signals are processed and an inverted phase sound wave with the same amplitude as the original sound is created. This new sound is converted into an analog audio signal and output by the DACMC internal tone generator to all of the speakers except the instrument panel center speaker (if equipped).
It doesn't work quite like noise-canceling ear phones, where it cancels all sound external to the ear phone.
It looks like the only possible way to know if it is working or not, would be using the IDS software tool.
There are several diagnostic trouble codes associated with the active noise cancelling system.
I have noticed on my C-Max that at times the ICE becomes suddenly louder as though the noise cancelling temporarily stopped working.