Without having actual experience, from doing some research, the prevailing answer is negative - you will get your FHR benefits, however no elite status benefits directly from the hotel as this will be considered a third-party booking (where / when / how you pay is irrelevant, what matters is the channel via which you book). Unless my understand is wrong, the only type of third-party booking that brings you both complimentary and elite status benefits is the one made through the Impresario program.