Well, you said it won't talk to
anyone, then you agree that of course it would talk to emergency services.

About turning off all radio, aside from WiFi, don't forget Bluetooth. In my phone, Bluetooth can be turned on/off independently of airplane mode and independently of WiFi off.
To recap,
- airplane mode, to stop the cellular radio
- Wi-Fi off, to stop the wireless network
- Bluetooth off, to stop BT and BTLE
- even shorter range, turn off the near field radio (NFC)
don't know what other transmitting ways are in the most recent phones, my smartphone is ancient.
I've never tested if this means complete radio silence, or if the phone first boots normally then applies the settings only after the OS is running.
Wondering about this because, for example in my provider's router, there is a WiFi-off settings, and it even has a physical button for that (aside from the SW setting). Though when the router boots, it still turns on the WiFi for a brief second before the WiFi-off settings are applied. It has a LED that shows WiFi traffic, which blinks a little, and it transmits something, I've seen the Tx signal while fooling around with a PlutoSDR.
Another thing, I'm curious if a phone would still receive SMS/disaster alerts in airplane mode. AFAIK the SMS disaster alert should work without SIM, but should it work in airplane mode?