Yes and no. It depends on what device you're using, and which version of the app. Most versions of Textfree can send messages when not connected to a network but will be unable to receive messages unless they try again once there is connectivity. Before sending a message while offline, hold down the message (don't swipe it away) to see whether it was sent or not. If it was successful, you'll see a "Sent" banner at the top; if it didn't go through, there won't be anything except the Send button itself after releasing your hold. You can also re-send the message while online to make sure it goes through, or delete it from the Sent folder (since you can still get them if they came in.