Not on the room reservation only, but you can potentially "double dip" if you want to splurge on dining and other services at the hotel:
- Book and prepay the reservation to get the $200 Platinum FHR credit.
- Spend over $500 on incidentals (actually more like $600+ because you'll probably get $100 credit as an FHR benefit), charge it to your room, and pay that final balance with appropriate Amex card to get the offer credit.
The one caveat is I've been at hotels that are sticklers about FHR program and using Amex Plat. card to close out the folio (even if you're prepaid the room w/ the Plat. card). I think as long as it's any Amex card, it'll be fine. But ideally you'd added the Peninsula or other hotel chain specific offer on the Plat. card as well to avoid potential issues.