Use the kill switch, Luke. 
I always HK WiFi before leaving the house. Why transmit probes and who knows what else if you aren’t intending to use WiFi? If nothing else, it should reduce power consumption and extend the time between charges.
That is true but it is not necessarily as precise as GPS, such as may be obtained by an app and then transmitted by an app (or recorded on the device by the app or by the underlying operating system for future use by the government).
Perhaps though in the case of Capitol Hill, it is littered with Stingrays. 
It does come down to as @danielr says: if you plan to break the law, don’t take your tracking device with you. However I would go further: even if you plan only lawful protest, don’t take your tracking device with you.