If you book a hotel other than their own website 99% of time they won’t honour anything. So there is no chance those nights will count towards anything and won’t receive any points either. The hotel might consider that other benefit can be used such as lounge access or free breakfast etc but that is down to the hotel itself. I would email or call the hotel if you already have a booking and ask to add your membership status and see what they are saying. If you want 100% guarantee than you have to book the room with them directly.