No. You do not earn the hotel points. The major hotel chains have all established new policies where they only give points when a room is booked through their own websites. They don't provide points when booking on any outside booking engines. If you book on Expedia, Travelocity, Orbitz, etc. you don't get the points.
If you make sure they attach your reservation to your hotel reward number you still are earning your status with the hotel because you are credited with the "stay," but you are not earning their points for free rooms at their hotel.
You get something much better: Xpirient Reward Credits, which can get you free rooms at that chain but also any other travel related booking in our platform.
Thanks for being a valued Xpirient member.