We are using AJAX search with category boxes in our recipe page. It works great, but when you uncheck a category that had been checked the results don’t repopulate with the default list of all posts.
The auto populated results can be different from the ones that you get from a triggered search. The reason is the different ordering. If you want to get the same results, then set the auto populate to an empty phrase: https://i.imgur.com/jweJL9R.png
Then the initial and the unchecked should be the same.