Emacs does this thing with search where if you search for something that contains any upper case characters then it does a case sensitive search. If somebody is searching for mFoo, they probably don't want matches for mfoo. I suppose this is a matter of taste, but I find it handy. The UI might be a little confusing on SearchFox, when it has the checkbox.
I guess Searchfox could automatically check the "Case Sensitive" box the first time you type an uppercase letter in the search box.
Yes, that would work.