Indeed. And on a Google-free Android phone the XMPP client Conversations can utilize its existing, permanent XMPP connection to deliver push notifications to other (mostly open-source) apps using an alternative to Google push (FCM) called UnifiedPush.

There was a talk at FOSDEM about that.

https://gultsch.video/w/gRGZqKKvNBvvMesyWNQzoK