Ring dev here.

Ring send messages via the DHT. The DHT stores them for a certain amount of time, which depends on the current traffic. But in general we can send messages, go offline, and have it received even if the receipient joins the network 10 minutes after.

This is configurable and depends on a lot of factors, but should the network be generous enough to store every offline message you want it to store, you could send messages with hours of interval.

However, there is currently no guarantees. Only by being online you can ensure that your message goes trough.