SMS is sent in an area called the "control channel" that follows along side the call, so it MUST use the cellular network in order to function, however you can send an e-mail to PHONENUMBER@vtext.com such as 1234567890@vtext.com or to the carrier's default. Search Google for send text message from e-mail.
You can also use some other applications that allow you to buy text messaging "credits" that go over their network.
Chris