Goodwill points come out of a completely different account. Clearly, it would be inappropriate for hotel x to limit goodwill points based on the fact its a reward stay.
As others have suggested, hotels pay very little for free night awards. I have seen the invoices at its typically well below $100.
(If you really want to know the amount, look up the court docs filed in the recent dispute between Starwood and -I recall- the St. Regis in NYC!)