I don't think so. A "notification service" isn't something that exists solely on the user's device; there's also a server-side component that each remote service that wants to send a push notification has to interact with.
So for Android to support alternate notification services, every app/service that wants to send push notifications would _also_ have to support those alternate services on their backends.
So for Android to support alternate notification services, every app/service that wants to send push notifications would _also_ have to support those alternate services on their backends.