What I can say about this is that at LAX while I was checking in with Qatar Airlines, I was asked to show my ThailandPlus app. They also checked to see that Ihad already registered it. Also on the very bottom part of my COE it dose clearly say ( see attachment) that you do need to download and register the app. That being said when I arrived here in Phuket the app seemed to have stopped working. A friend who came on Singapore Air was not check for his Thailand plus app.
For the cost of a cheap smartphone it seems that it would be somewhat ill advised to make the trip without being 100% prepared or in compliance with what is so clearly stated on the COE. As most of us all ready know when dealing with Thai immigration it’s always a good idea to be well prepared.
good luck