You'd break the fast with BPC anyway. Yes you can.
BP IF actually refers to ketosis, not really 'fasting.' A bit of marketing.
You can eat/drink fats and your body still stays in ketosis. If you were to take in something that elevates your insulin levels you would stop burning fat as efficiently. He just means what kind of fat burning state you are in or how deep you are. For more thorough information on intermittent fasting check out www.leangains.com