No, but the only room you can book with cash on Sept 21, 22, and 23 is the Presidential Suite for 6.1k EUR + tax. If you want to stay at the Intercontinental Athens on those dates you can book a standard room with points which would save you several thousand dollars vs booking with cash.

You won't receive the same room with points as cash, but the only alternative to points is cash and if you were to book a room with points your points are basically worth 15 EUR cents each based on how much money you'd save.