Hi!
Yes, that explains it. For very old IE versions (IE<=9) the plugin simply outputs the default WordPress core search box (or nothing) instead as a fallback. The compatibility mode on IE edge is also a problematic feautre, as it's not the same as viewing it with previous original IE versions. I had to set up multiple virtual machines with pre-installed windows versions to be able to test. I believe about a year ago, when Microsoft finally discontinued IE 10, 9 and older, we could officially move on and simply use a fallback method, except for IE 10, which is still capable of displaying most features of the plugin just fine.