Will iPhone change its timezone automatically if I fly on an airplane? Let's say, I have time settings set to automatic update.

With airplane mode on and off (both cases), would my phone update timezone automatically?
If your iPhone finds your location and you're in a new time zone, it'll change the time.

With Airplane Mode off:
Your iPhone will be silently using location services and will update the time based on your location change.

With Airplane Mode on:
GPS and Cellular (two of the three methods an iPhone uses to determine your location) are disabled, but you can enable wifi still. Even without connecting to in-flight wifi, but as long as there is in-flight wifi, your iPhone can determine a time zone change based on location info provided by that wifi network (which Gogo inflight does but I'm not sure about ViaSat).