At its core, Pulse SMS is just a normal SMS app. If you have no signal on your phone (zero bars), the app will not be able to send messages, regardless of what device you are trying to send from. Your phone must also be turned on for messages to be sent.
There is one exception to this, but your personal usage may vary. Some carriers have Wi-Fi calling that you can enable/disable at the system level. With some devices and carriers, enabling this will allow you to send messages over Wi-Fi alone. You will need to test this for yourself to see if this functionality works in your situation. We're not able to provide a complete list of carriers or devices that this will work on.