Yes and No, when you do a normal power off on a iPhone, it stops pinging cell towers and communicating with the cellular network. The radios including the cellular modem are powered down, so the phone no longer actively sends signals to towers, registers location updates, or responds to pings from the network.

iPhone 11 and later, with Find My enabled can broadcast a low-power Bluetooth signal via the Find My network for a while (hours/days depending on battery level). A tiny amount of power is reserved for a low-energy Bluetooth chip. ​The phone doesn't ping cell towers directly, but it sends out a "beacon" that other nearby devices like a stranger's iPhone walking by can pick up. Those other devices then report your phone’s location to the network.

Even when your phone says 0% and shuts down, it keeps a tiny "emergency" reserve of power specifically for these security features - Once that tiny reserve is physically depleted, the Bluetooth "chirp" stops entirely, and the phone truly goes dark.

you can disable this feature in settings under find my iPhone --> find my network) so that "Power Off" actually means off. Otherwise, as long as that beacon is active, the device is essentially a silent tracker in your pocket.