They’re still running in low power mode and can wakeup from the network so they can absolutelly be made to “boot up” without turning the screen on and you being aware of it.
This is not like a bloody PC were the lights turn on and you can hear the fans when the thing starts, it’s a machine with a low power mode in which it can already do a lot and which can be brought to a high power mode if needed without there being any visible or audible side-effects to alert the user.
Unless you completelly cut it off from power (by taking the battery out, which you can’t in most modern smartphones) that smartphone with the lights off, the screen off and making no sound at all can just as easilly be in low power mode waiting for you to press the On button, as it can be in full power mode with a mobile network connection active, accessing the microphone and the GPS microchip and sending that data out, and both will look exactly the same from the outside.