I think it's an interesting problem. A server running in low-energy mode most of the time would miss any incoming messages.
So you'd need a way to signal to other servers that your low-energy server is back online, and wants to collect any incoming messages.
One way to notify them is by delivering outgoing messages. We should probably make a best practice that if you're doing exponential backoff, and you get an incoming message from the server, it's a good time to retry.