It seems so.
He doesn't really want to detect cell phone usage, he wants her to not run up thousand dollar phone bills and to get enough sleep at night. As long as it isn't a financial burden and it doesn't affect her school performance and mood, he doesn't (or shouldn't) care whether she's using a phone at a given time.
I don't have any experience in the care and feeding of teenagers, but I guess I'll join in stating what my intuition tells me with the limited knowledge I have of the situation. It seems to me that taking the phone away outright was the wrong response. Maybe for a set time it would be good (that was a really big phone bill), but I think it would be better if she could be made to pay the cost of her bill, at least above a certain amount. However, if her only source of income is allowance, this is trickier, and I don't know if you can backtrack to this point now that you've passed it. Also, you could say the underlying problem isn't the time and money, it's her lack of respect for you. There's no way to confront that directly, though, so you're better off chasing the money.
TL;DR: Becoming a financial drain on the family is the perfect opportunity for a harsh lesson in financial planning rather than an expansion of domestic spying powers
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