Indeed. It seems FluffyChat (Matrix client) can now use Conversations for push notifications delivery.
(Trying to wrap my head around the architecture too, with the last sentence there. Presumably the service and client need to know how to talk to the UnifiedPush provider?)
And XMPP is just $lightProtocolB, there is nothing stopping an XMPP-based UnifiedPush distributor w/o messaging from existing. If you don't use XMPP for messaging, there are many simpler distributors available.