No. Your son's phone can even be completely off. It doesn't matter.
Did you use the tracfone app in your phone to add data to your son's line?
That's what I do with a phone that I almost never have physical contact with but I manage the line from my phone using the TF app.
I'm sure you could also do it using your phone browser (if you don't have the app and/or you phone is not with tracfone).
All I care is that when I check the balance for that line, it shows the minutes, texts and/or data being added to it. If they don't show after you add them, the issue is not related to your son's phone lack of connectivity to wi-fi or data at that moment, or you not using wi-fi either for the transaction.
I've never had a problem with doing it that way.
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