You absolutely can pay with another amex product according to FHR rules. Green, Gold card, SPG, etc. So unless the hotel is advised that you no longer have a FHR reservation I do not think you will have a problem. You certainly are skirting the rules and spirit of the program.

All of that being said I think almost anyone can get FHR benifits or cash equivlents ( A discount, or freebee like breakfast) in todays hotel market without FHR.