When I have booked via the AA hotel portal, which would be no different, I get my Marriott confirmation number (separate from my Advantage Hotels confirmation), and enter it in my Marriott app. 100% of the time I have been welcomed with the status I have, given those benefits, including, for example, free high speed internet--even at hotels where they charge for all of it (which is bizarrely still a thing).
As cfischer notes, this is not guaranteed, but Marriott is really great about doing this. Recently, I have found Hilton has done likewise. (Clearly I am trying to lock in that AA status!)