I have found with latest iOS (11.2.1), iMessages does *not* work on iPhone 7 or iPhone SE with wifi off and airplane mode on when using the ethernet adaptor. Safari does and email works though.
Also, an Ipod 5 running 9.3.5 iOS works with iMessages over ethernet (wifi off, but airplane mode needs to be off. appears odd since it has no cellular/wifi to utilize).
I see no reason technical reason why iMessages/facetime can't be engineered by Apple to work over the ethernet adaptor for the iPhone since it already does on iPod.
Apple - please update iMessages/Facetime to work with ethernet adaptor for iPhones (it would be much appreciated - I did spend a small fortune on your products because I thought from reading these forums that iMessages *did* work on iPhone over ethernet).
Thanks