Both have to be online to transmit messages. As there is no server.
More or less how skype used to work, before it got bought by Microsoft and centralized.
I use signal to chat with my cousin who is in another continent, and he is online only when within reach of public wifi when he's outside, which is at night for me. My phone is always connected to 4G, so maybe what you propose could work in this specific case, but in other cases it could be an issue.
If that was the case, you'd use email, not a realtime chat platform.
And keep in mind, it was never an issue with the old, decentralized Skype.