Don't know if this data point helps. I stayed at a Thompson and booked through Hyatt. My plans changed to stay through the weekend. After seeing how much it would cost to change my reservation, I ended up booking the extra night at the hotel through AMEX Hotel Collection (prepaid of course). I received the $200 credit next day or so. I was unsure if I would earn night and dollar credits for this second booking.
The front desk offered to merge the reservations upon checkin. I was ideally looking to stay in one room throughout the stay but needed a second bed for the extended stay. It wasn't really a big deal one way or another. Hotel ended up upgrading me to a corner suite with a pull out couch for the four nights. I'm a Globalist so that probably didn't hurt the situation. I had one folio and didn't have to check out/check in in the middle of the trip.
Hyatt provided me credit for the full stay and the entire amount I spent on the rooms. I was happy to learn that I can use the $200 FHR/HC credit and still receive the benefits.
Breakfast was included and I didn't really spend any money at the hotel so I have no idea if the $100 credit mattered or not.
One hiccup is that I originally presented my Hyatt card after the front desk merged the reservations and processed the upgrade. But then had to change to my Platinum card to get the $100 benefit per the agent's request. I didn't care much either way. I noticed that the first set of nights was charged to my Hyatt card and assumed incidentals would then all go to Platinum. I had a question at checkout about my folio and the desk ended up refunding the charge to my Hyatt card (wish they hadn't) and put that and the incidentals on my Platinum. When I say incidentals, I mean the tips for breakfasts. I'd keep my mouth shut if I had to do it again, but there was an error in my folio which got resolved and resulted in spending less money.
I share this level of detail because the question I cannot answer is would I have received the credits if it was a stand alone AMEX HC booking.