Hi,
Yes, you are correct. The Wireless UART example sends the information received from the serial terminal over the air. For the modification you made, your information will be sent until you receive it through the serial terminal
Now that you can send to your cell phone, what you have to do is use a timer so that you don't need to wait for a stream through the serial terminal, and you can send your data over the air.
Hope this makes sense.
Regards,
Ricardo