I'm pretty sure that the Ody's and Pilots with VCM also have ANC. Somewhere in the vehicle there is a unit that processes the input from the microphones and creates an anti-noise signal to cancel the offending noises out. I am not sure if this unit is part of the stock audio head unit or just uses it as an amplifier. However, I am almost positive that there are some ANC diagnostic functions that are accessible from the head unit which suggests to me that it also contains the ANC processor.

I can't imagine that replacing the stock speakers would cause any problems. It might even help.