get_template_part in admin

Yes, get_template_part() does work on Admin pages. Here is how I tested:

Add this to functions.php theme (or child theme) file:

add_action( 'admin_menu', 'wpse_99662_register_admin_test_page' );

function wpse_99662_register_admin_test_page() {
    add_menu_page(
        'Admin Test Page',
        'Admin Test Page',
        'manage_options',
        'admin_test_page',
        'wpse_99662_admin_test_page'
    );
}

function wpse_99662_admin_test_page() {
    echo '<h2>Admin Test Page</h2>';

    get_template_part( 'admin', 'test' );
}

The admin-test.php file contains the following:

<?php

echo "Loaded admin-test.php<br />";