Check to see if Omeka main public nav has submenus.

submenu-check.php

<?php 
    $nav = new Omeka_Navigation;
    $nav->loadAsOption(Omeka_Navigation::PUBLIC_NAVIGATION_MAIN_OPTION_NAME);
    $nav->addPagesFromFilter(Omeka_Navigation::PUBLIC_NAVIGATION_MAIN_FILTER_NAME);
    $view_nav = get_view()->navigation()->menu($nav)->getPages();
    foreach($view_nav as $page) {
        if($page->hasPages()) {
            echo 'has submenus';
            break;
        }
    }
?>