But it wouldn't matter anyway, that other party in the communication could easily be somewhere with phone service but no data. Or someone in the group sms could be on a non apple device. Boom, Just like that, your communications have been sent to multiple carriers, including your own. Those carriers all pinky swear that they won't do anything bad with your sms though. So I suppose it's not that much of a problem. /s
Why would anyone use a public network to communicate in secret? If you have a need for stealth communication with another individual, (maybe you're a dissident or what have you), then you should use the proper techniques. And, yes, keep your data encrypted on your own iPhone. Do not back it up to iCloud. Or Amazon Photos. Or Backblaze. Or Dropbox. Or etc etc etc.
Oh, and never, ever, use Android. You likely don't have the technical know how to make a commercially available android device private.