"No Cell Coverage" drains iPhone battery even when cellular data is turned off
I'm using my iPhone SE internationally, and even when I turn cellular data (and roaming) completely off, my battery drains rapidly and "No Cell Coverage" takes up most of my battery usage. I'm running iOS 10.3.1.
One solution would be to use airplane mode, but airplane mode appears to eliminate my ability to make calls over wifi, even if I turn wifi on while in airplane mode.
At various times, I've turned cellular data on and off and restarted the phone, and that action has sometimes stopped the "No Cell Coverage" battery drain for a while. But then the problem returns.
In short, why is my phone searching for cell coverage when cellular data is turned off?
iPhone SE, iOS 10.3.1