I have read about people stacking it successfully with 3rd night free benefits. I suggest trying it by booking the 4+ night stay through Citi Concierge and then calling Fairmont with the confirmation and try to apply the 3rd night free to the 3 nights you are paying for. Once you have confirmations on what you are paying from both , you should be good. I have never heard of Citi re-calculating anything after the fact. They give you an upfront calculated reservation showing you paying for 3 nights. What happens after that regarding benefits should not be their concern.
I have used the 4th night free a couple times but not with trying to stack it.