For room bookings via agent websites, you may find that when you check in they refuse miles, but if you retrospectively claim them, they will subsequently give you miles.
In theory, it's the same as buying a deeply discounted air ticket, regardless of what you have actually paid and how they compare to the best available rate at the hotel itself. I've not experienced this problem at the Radisson Edwardian, but I have at the Sofitel in New York. It also depends on the check-in agent you have and what they are able to do.
I always try and book on the hotel site, but sometimes the rates to be had elsewhere are just too good to refuse, so you take a risk when you don't buy from the hotel.