Integrated Messaging synchronizes between the devices. I don't think messaging from one is dependent on the other(s) being powered on.
We understand the importance of being informed about the possibility of sending messages from your laptop without having your phone powered on or having it in Airplane Mode.
Regarding your question, you can definitely send messages from your laptop without needing your phone. The following link will guide you through the process of sending messages on our website. http://spr.ly/6606EcW7j