I wouldn't say they "never" will offer last minute deals, but it isn't their norm. With that said, it is still very possible for less expensive rooms to become available. RPR has a lot of conferences and other block reservations that hold large groups of usually lower priced rooms. If all the rooms in those blocks aren't reserved by a certain date before the stay (often about 4 to 6 weeks before the event dates), they will usually be released back into the hotel's general inventory at their normal prices. And of course people make and then cancel reservations all the time.
So it is very possible that lower priced rooms might show up, but to get one of them you need to be checking at least weekly if not every few days. Others may want those lower priced rooms as well and they may get those rooms before you would if you aren't vigilant in watching for those rooms.