Yes this is possible. Either using a custom plugin or a quick change to the qa-page-user.php file inside qa-include folder and here is the change:
Below line 56 (and above the switch case block) add following code:
if(qa_get_logged_in_userid()===null) {
$qa_content=include QA_INCLUDE_DIR.'qa-page-user-not-logged-in.php';
break;
}
Where qa-page-user-not-logged-in.php is your custom template file that you need to create. However this is just a quick n dirty way and you should try to convert this into a plugin by overriding layers and modules.
