Does the app work without WiFi or data connection?

Nope.

We'd love to be able to let you use Textfree without WiFi or a data connection, but it technically isn't possible.

WiFi, and data plans from your cellular provider, are what connect your device to the internet. 

Textfree uses the internet to give you FREE texts (and calls too!).  

Without WiFi or a data connection (the internet), your device can send and receive texts and calls as well as one of these: