No - booking fees need to be paid by credit card and can't be covered with points. This is standard across most airlines and travel providers, where a flat booking fee and processing fee apply any time points are redeemed.
The Processing Charge covers those booking fees, along with processing on whatever portion you pay by credit card. So if your points don't cover the full cost of your booking, we'll only calculate the Processing Charge on the remaining amount you're paying by card - never on the points themselves.