#5491 Si tienes cuenta de activision es de suponer que sí, porque logeas con la misma cuenta y tiene crossplay.
Sacado del faq:
Game progress in Call of Duty: Modern Warfare and Call of Duty: Warzone is stored on your Activision/Call of Duty account, not your platform account. That means your progression carries with you no matter which platform you play on as long as the platforms are linked to the same Activision/Call of Duty account.
Cross-progression includes XP and Weapon XP, items you've earned or unlocked through gameplay, Battle Pass progress, Campaign progress, and Missions and Challenges you've completed.
Cross-progression does not include Call of Duty Points (CP), however. You can only spend CP on the platform on which they were purchased, but items you purchase with CP are shared across all linked platforms.
Please note: If you choose to link a platform account to another Activision/Call of Duty account, your progress will not carry over.
https://support.activision.com/call-of-duty-warzone/articles/crossplay-and-cross-progression-in-call-of-duty-warzone