Solution used:
// decide to show or hide the widgets
function check_for_using_template(selected){
if (selected == "page-templates/core-front-page.php"){
jQuery("#page-core-home-1").show();
jQuery("#page-core-home-2").show();
jQuery("#page-core-home-3").show();
jQuery("label[for="page-core-home-1-hide"]").show();
jQuery("label[for="page-core-home-2-hide"]").show();
jQuery("label[for="page-core-home-3-hide"]").show();
}else{
jQuery("#page-core-home-1").hide();
jQuery("#page-core-home-2").hide();
jQuery("#page-core-home-3").hide();
jQuery("label[for="page-core-home-1-hide"]").hide();
jQuery("label[for="page-core-home-2-hide"]").hide();
jQuery("label[for="page-core-home-3-hide"]").hide();
}
}
jQuery(document).ready(function(){
check_for_using_template(jQuery("#page_template").val());
jQuery("#page_template").change(function(){
check_for_using_template(jQuery("#page_template").val());
})
});
Unfortunately, I was unable to successfully utilized the is_page_template, so I used jQuery. Works, though it may not be the most efficient solution.