This is not entirely correct. Messages are stored on their servers temporarily (last I saw, for up to 30 days), so that even if your device is offline for a while, you still get all your messages.

In theory, you could have messages waiting in your queue for device A, when you add device B, but device B will still not get the messages, even though the encrypted message is still on their servers.

This is because messages are encrypted per device, rather than per user. So if you have a friend who uses a phone and computer, and you also use a phone and computer, the client sending the message encrypts it three times, and sends each encrypted copy to the server. Each client then pulls its copy, and decrypts it. If a device does not exist when the message is encrypted and sent, it is never encrypted for that device, so that new device cannot pull the message down and decrypt it.

For more details: signal.org/docs/specifications/sesame/