iMessage uses Wifi or Mobile data. It's not an SMS, it's a service provided by Apple for data networks. Is there a particular reason you are turning data off? iMessage uses minimal data unless you're sending/receiving large pictures/videos.
Apple 6, latest OS version
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My daughter complains that while the data is turned off she cannot received text messages from anyone who is using iMessage. Even though her data is turned off and she is not using iMessage, why can’t she receive them in SMS format ?