Recording Ambisonic Sound with BMPCC4K

I plan to use a Zoom H3 w/ a BMPCC4K to record ambisonic sound. I want the sound to be recorded w/ the SD card inside the BM4 so the sound will by synchronized.
Will the camera record all four channels of H3 audio?
If so, will the in-camera mics still record?

The Pocket cameras can record only two channels at a time.