Not if the mobile plan has no data. I assume the parents are paying for the cell phone, so have control over that.
Hopefully there were familial communications breakdowns that led to this, and it isn’t a father who is just being a dick. (I mean, he’s still being a dick because he’s taking out the entire neighborhood, but I hope he tried the more normal asking-and-if-that-doesn’t-work-demanding approach first, before firing up the jammer. And, to be honest, there are next steps many parents take that are far worse than what this parent tried.)