No, Firebase Cloud Messaging is a separate service from Play Store. As long as the device has Google Mobile Services installed the app can be installed from anywhere and doesn't need to be uploaded to Play Store.

Yeah that’s a big requirement. To get Google mobile services, you’re required to install Google chrome, Google play, and bunch of other bloatware.

You don’t have to load the app via Google play but your device needs to be managed by Google.

Which would be fair game except to my knowledge there’s no API in iOS that enables the use of anything other than APNS for notifications. I could be mistaken though!

Again, I don’t see how that is different from android.

For android, you need to buy into all the ecosystem of Google to access their push notification service.

You can use android without google’s system, but you can’t use google push system.

Because on android you can install another background service that can replace the features of the google service. This is pretty much what the Chinese did when they forked Android. There are alternative app delivery/update mechanisms that make this point entirely moot.

On iOS you just can't unless you are fully blessed by Apple, and this is precisely the issue.