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Are you referring to messages+? If you are there has been a lot of complaints about this app using a lot of data. I am not sure if they got the bugs out of this app but there are a few threads still on here about this app.
I am not sure about message+ but I have a S7 edge and use the other messaging app that came with my phone. I have my mobile data off 99% of the time and I am able to txt just fine with my phone being on WiFi.
Not sure about other messaging apps but we also have a S5 that is not activated and we can use messenger the facebook app on it using WiFi and those txt go out fine too.