I'm not sure what you mean but no, it won't work with chords, if a chord is played, the loudest note will be counted.
I wondered what would happen if both of the two notes are exactly the same amplitude so I did a simulation and if it's positive edge triggered, the lowest frequency is counted, if it's negative edge triggered the highest frequency is counted.
The phase also makes a difference as to which signal is counted, if the low frequency signal is shifted by between 90o and <180o and positive edge triggering is used, the highest frequency is counted, a phase shift of under 90o and the lowest frequency is counted.
I suppose this means that in reality, the result will be unpredictable: with a chord you could get either note.