Yes, you do get concierge privileges if you stay in a suite in Tonga. I am not aware of a specific Honeymoon suite there, but since Tonga was recently rehabbed, perhaps they are calling one of the smaller one bedroom suites (Princess suites?) a Honeymoon Suite now (or perhaps I have no idea what I am talking about, lol).
There is a small amount of snacks and drinks out in Tonga (like concierge light) and you can access the Hawaii concierge lounge for their offerings as well. I also believe they will stock your favorite drinks in your suite fridge. (can anyone confirm that?)
I have not stayed in Tonga yet, but have ressies for a two bedroom Princess suite for October, my info is simply what I have found while researching for our upcoming trip.