No, you don't. You have to actually stay (pick up your key from the front desk) to have points/stay records.
This is a pretty definitive statement. IMO it should read that you "should" have to actually stay (pick up your key from the front desk). I would agree with that statement, because that is how it should be. However, I've personally received points from a stay without being anywhere near the hotel. I called and talked to the hotel, someone checked me in and I never even went to the same city the hotel was located in. Received credit and points for the stay.