Not to be contradictory, but notifications do NOT "go through" g* or anything else. Notifications are a function of the operating system used to alert the user and they are totally private except to people who can actually SEE the screen. The reason for the alert could be a local condition, such as an alarm clock, or they could be data sent from some server, which may be g* if you have your phone set to use that (g* is themselves trying very hard to force network services to route their alerts through their servers, but it is NOT actually necessary), or it may be some other server.
FCM is not notifications. It is a route that can be used to pass messages via g*, which may or may not even result in a notification.