Yes. Marriott has their "No Blackout Dates" for award rooms, but that is different from "last room available." Starwood's program, SPG, advertises the "last room available" benefit, but Marriott does not.

My understanding is that each hotel has to offer at least a certain percentage of rooms for awards each night. I don't know what that percentage is and I don't think Marriott has ever published it. Of course a hotel could offer more than the minimum, but they don't have to.