I doubt they would know. Read the terms of your loyalty program to see which booking channels are excluded.
They don't really know.
I booked twice through them. One for IC NY Times Square, one for IC Chicago Magnificent Mile. Same rate type which requires one night deposit. Those rates were published on the hotel website, so I was able to compare their quotes with the hotel website price.
First time, they gave me a quote for IC NY, exactly same as the hotel website, including the cancellation policy. I was also able to add my IHG Rewards Club member number to the reservation through the phone and the reservation showed up on IHG website smoothly.
The second time, they gave me a quote for IC Chicago, exact same total price but saying the cancellation policy is totally non-refundable. I doubted it and had them double checked it and they insisted that full deposit is required at the time of booking. And they claim that, because the booking is made through them, I wouldn't be able to add the membership No. to the reservation. I accepted their "non-refundable rate" anyway and made the reservation. Immediately I contacted IC-Chicago, and the hotel staff was able to add my membership No. and confirmed it's point & stay eligible. The reservation appeared online shortly after adding my membership No., and it turned out to be the same one-night deposit cancellation policy as my first booking. So the travel agency got wrong on the cancellation policy stuff, and also the membership number.
I was also able to add my HHonors number to a Conrad hotel booking. So this seems to depend on which representative you got on phone.