Shouldn't be possible.
The act of requesting to LISTEN requires doing a sort of update to the database. In elder versions, it put tuple(s) into pg_catalog.pg_listener, and that's Right Well Disallowed on a WAL-based replica.
I would think that if you're keen on building an "event detection substrate," particularly one that's supposed to cross clusters, then you should consider using something actually attuned to that, such as a message queueing system, whether an AMQP implementation such as RabbitMQ, or a message bus like Spread. If you do that, then you can do this in much broader cross-cluster ways for unrelated Postgres clusters.