You can but you shouldn't
FCM token can change if you see the Service used for getting the FCM token, the one that has to extend FirebaseInsanceIdService the method inside is called onTokenRefresh() because it will be triggered every time the FCM token is refreshed for a new one. In previous Google Cloud Messaging (GCM) this strike to me as erratic, but in current FCM it seems to be infrequent.
You could do this by saving the current token in some form of local persistence (sharedpreference, database, etc). Then when the FCM is refreshed using the stored FCM the nodes in the real-time database can be updated.
This will have some bad scenarios: what happens if the user re-login by reinstalling or changing device? The first can be solved by saving something unique in the device, I have seen that some sort of devices ids can be get, but those are reset after boot or factory reset. Then a more general solution would make the user to input something unique to them every time they log in. It could be the email, or it could be the phone number.
Which leads me to, use phone authentication instead