Only when the kill switch is on. I control it.
Also, it's possible to get AweSIM service hiding your data from the mobile operators.
We should be enforcing informed consent regulation of network infrastructure, treating privacy and anonymity as synonymous with liberty and freedom. Allowing the system to operate as it does is a choice; those with lots of money get to make it grow by exploiting a constant invasion of privacy with no concurrent return to the society being exploited.
Phones aren't built to be privacy respecting, and kill switches are a mitigation of a symptom, they don't do anything to address the disease.