According to Verizon (a large company generally positioned to be a trusted source of knowledge for how cellular phones and cellular networks work):
When using Wi-Fi Calling, 911 calls will always try cellular service in the local market first, even when the device is in Airplane Mode or cellular service is off. If cellular service isn't available and the user has set up Wi-Fi Calling, the 911 call will route using the registered address.
If a cell phone is in Airplane Mode with cellular service disabled, how can it connect to cellular service in the local market? Under what other conditions might cellular transmissions happen despite the user's efforts to disable cellular transmission capabilities?
Consistent with the explanation of cell phone user interfaces (which should be an authoritative source about what the feature does), similarly positioned wireless network provider SaskTel explains, unqualified (as far as cellular service is concerned), that
Most wireless phones and devices have a setting that allows you to turn off all network connections. This might be called "Airplane Mode," "Flight Mode," or there might be an option to "turn off all connections." When this mode is on, your phone can't make or receive calls or text messages, or access data services such as email or the Internet.
The conflict between these claims is central to the present question.
It could be useful to know what conditions override settings for Airplane Mode and cellular service, both for concerns one might get after reading a lot from Edward Snowden or news about SCIF-storming and/or thinking about potential impact of intentional transmitters on commercial aviation. (I assume that for example, accurate perceptions of strong emergency situations aboard commercial passenger aircraft are likely to be highly correlated among a relatively large number of passengers; it would be unfortunate if that led the emergency to be exacerbated contrary to clear UI labeling.)