How to display content If function exist/condition true?

You’ve got an issue with your code. This code will always return true because you’re passing a string to it.

if ('custom_header_display') { ?>   
    //my code
} ?>

You can instead use is_plugin_active() to check if the plugin is activated.

Quoting the example from the Codex page, your code should be like:

<?php

include_once( ABSPATH . 'wp-admin/includes/plugin.php' );
if ( is_plugin_active( 'plugin-directory/plugin-file.php' ) ) {
   // include your file.
}