Assuming the rates are the same (sometimes the rates are different, and the OP hasn't commented as to this), I would guess the hotel management wouldn't care. But I would absolutely call the hotel, get ahold of a manager (not a front desk clerk), and clear it in advance. If the rates are not the same, then the perks also may be different.
The Marriott government rate at individual properties (which is supposed to be pegged to federal per diem absent some type of mythical waiver) is as a result of Marriott policy, not a contract with GSA, as others have mentioned.

A private organization called fedrooms (fedrooms.com), which has some sort of relationship with GSA, does sign contracts with hotel chains and individual properties, but GSA is not party to such. Many Hiltons, Intercontinentals, and Starwood properties are in the Fedrooms program, but very, very, few Marriott properties.