Yes. Take that exact code and put it into the tpl_main_page.php file near the bottom (just above or below the "google analytics" require file.
Insert it as follows to only show on the checkout_success page and you should be ok.
PHP Code:
<?php
/************* bof AdCenter Tracking Code ********************/
if($page_directory == 'includes/modules/pages/checkout_success') { ?>
INSERT YOUR TRACKING CODE HERE
<?php
}
/************* eof AdCenter Tracking Code ********************/
?>