No. You cannot play multiplayer in Call of Duty: Modern Warfare II (2022) without an active Xbox Live Gold subscription (or Game Pass Ultimate, which includes Gold).
Free-to-play games like Fortnite, Apex Legends, and Call of Duty: Warzone do not require Xbox Live Gold for online play. However, the premium Modern Warfare II multiplayer suite is not free-to-play.
To access standard multiplayer modes, you must purchase an Xbox Live Gold or Game Pass Ultimate subscription.