Conditional Custom Image Header

by

you could try the following right before you call the body_class() function:

<?php
$header_image = get_header_image();
if( !empty( $header_image) ){
    $custom_body_class="has-header-image";
} else {
    $custom_body_class="no-header-image";
}
?>
<body <?php body_class($custom_body_class); ?>>