Check asset status (publish/unpublished) in Asset Finder on Page load (AEM 6.2)

Try this

(function ($, $document, author) {

    "use strict";

    $document.on('foundation-contentloaded', onAssetFinderLoad);

    function onAssetFinderLoad(){

        $.ajax(author.page.path+ "/jcr:content.json").done(checkStatus);

   }

    function checkStatus (data){

        var q = data["cq:lastReplicationAction"];

        if(q && q == "Activate"){

            $( "input[type=radio][value=Activate]")[0].checked = true;  // use a different selector for radio buttons in case of a conflict/customization

           $( "input[type=radio][value=Deactivate]")[0].checked = false;

        }

        else {

          $( "input[type=radio][value=Activate]")[0].checked = false;

          $( "input[type=radio][value=Deactivate]")[0].checked = true;

        }

    }

})($, $(document), Granite.author);

Add it under 'cq.authoring.dialog' category.

**This is just a sample code and not tested properly. Extend/Modify it per your use case to make it more specific.