Taking a look at the Rogers outage CRTC letter

This is likely going to depend on the OS implementation, since lots of OSes allow emergency calls even while the phone is locked (from the lock or password entry screen). My speculation would be that the emergency call would activate the cellular modem to do the emergency call, but as I said I'm not confident in that answer (and please don't try it to just test it out).

> Or would attempting to make an emergency call instruct the phone to attach to its home network?

That's a great question, I don't think I ever tried to do an emergency call while in airplane mode so I don't know the answer with authority.

This is likely going to depend on the OS implementation, since lots of OSes allow emergency calls even while the phone is locked (from the lock or password entry screen). My speculation would be that the emergency call would activate the cellular modem to do the emergency call and go back into airplane mode afterwards. But I'm really not sure and it's been a few years since I've looked at this.

> Or would attempting to make an emergency call instruct the phone to attach to its home network?

The phone wouldn't need to attach to it's home network first in any circumstance. Even when you're already connected to your home network, the device actually re-attaches itself in an emergency mode (atleast in LTE/VoLTE, I don't know about the older technologies I didn't work on). You would likely still use your own network, as the first frequencies the phone will be the frequencies in use by your own carrier.