Absolutely. In fact, you need Firebase Cloud Messaging in order to configure Facebook Push Notifications. If you see the content of the link https://developers.facebook.com/docs/push-notifications/quickstart, notice how under the heading "In-App Notifications", it says: "Prior to sending in-app notifications you will also need to integrate the FBNotifications library." Then if you go to https://github.com/facebook/FBNotifications, you will see that under the heading "Getting Started on Android", it says: "After you've added the dependency, you'll have to set up an FCM listener service,..." It is asking you to set up an FCM listener service and providing this link which contains the instructions to configure Firebase Cloud Messaging: https://firebase.google.com/docs/cloud-messaging/android/client.
Conclusion: Firebase Cloud Messaging is not an option if you want to configure Facebook Analytics Push Campaigns. It is required. Firebase Cloud Messaging can operate without Facebook Analytics Push Campaigns, but not vice versa.