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I would not be certain of this - the Amex Travel Agency is a third party site and there's probably a special non earning deal they have with the hotels.I expect you should still receive all published HH Gold member benefits. However, you should not be expecting the stay to earn any stay credits or points towards your HH account (except for non-accommodation spend such as restaurants, room service, movies etc).
I would not be certain of this - the Amex Travel Agency is a theird party site and there's probable a special non earning deal they have with the hotels.
There have been reports here and there of status benefits being applied, but one could not really be sure in this case.
I've had a chat with Amex today about this, as I tried to book a stay in Brisbane on the free Amex night, when the room class that they book into is available on the hotel's website. Amex wouldn't do it, as they were not getting any availablity through their consolidator. After the agent investigated and called me back, the agent mentioned that on this particular night, there is a lot of demand in Brisbane, and so most of the hotels have removed their inventory from consolidators on that night, preferring to sell them directly (at >$500/night). This suggests to me that they consider the Amex consolidator to be opaque channels, and so they may or may not credit it as a usual stay (with points, stay/night credits, and usual HHonors benefits. You might get them, but it wouldn't be guaranteed.