If possible, but that depends on what you want, you can use Realtime Database, but I think you would have a little problem in synchronizing both databases,
But in my case I would prefer to program my own Socket since I have more control of what I send, you do not need to program rooms or restrictions, it would only be a chain message every time the application is started and I would have it in a service.
You can also use Cloud Messaging and instead of using notifications, use it to send and update registration on all devices, but if you want you can also show some notifications for the most important events.
That in my case, but it depends on how you want to program it, you just have to have a bit of imagination, but in general the answer is yes