HH T&Cs have only one sentence that relates to your situation:
No Points or credit toward tier status will be awarded for "no show" situations when a Member has made a reservation guaranteed with a credit card but then does not check in to the hotel--irrespective of whether or not the Member's credit card is charged for any portion of the reserved stay per the hotel's "no show" policy.
In my view, you need to clarify directly with the hotel first what is their "no show" policy - based on that you will know what right to claim you have at your disposal.