Hi Daniele,
Unfortunately that won’t help. That option is only for cases where the results page is on a different permalink – but it still has to be the default wordpress results page.
WordPress will always handle the results page via the search.php template file in the theme directory. It might be possible to somehow custom code that template file for a conditional logic. The search IDs are sent via the $_GET['p_asid'] or $_POST['p_asid'] variables, that could be used to make separate loop layouts, in case you are planning to do that.