Query by one meta_key and sort by another (possibly NULL value)

I don’t think there’s a way to do it without using filters. Using posts_clauses you could do:

function wpse163696_posts_clauses( $pieces, $query ) {
    if ( $query->get( 'orderby' ) != 'dealer_date' ) {
        return $pieces;
    }
    global $wpdb;

    $order = $query->get( 'order' );
    $pieces[ 'join' ] .= $wpdb->prepare(
        ' LEFT JOIN ' . $wpdb->postmeta . ' dealer_pm ON dealer_pm.post_id = ' . $wpdb->posts . '.ID AND dealer_pm.meta_key = %s'
        , '_dealer_number' );
    $pieces[ 'orderby' ] = 'ISNULL(MAX(dealer_pm.meta_value)) ' . $order . ', MAX(dealer_pm.meta_value) ' . $order  . ', ' . $wpdb->posts . '.post_date ' . $order;
    return $pieces;
}

Then your query becomes:

add_filter( 'posts_clauses', 'wpse163696_posts_clauses', 10, 2 );
$customer_orders = get_posts( array(
    'numberposts' => $order_count,
    'meta_query' => array(
        array(
            'key'     => '_customer_user',
            'value'   => get_current_user_id(),
            'compare' => '=',
        ),
    ),
    'orderby'    => 'dealer_date',
    'order'      => 'ASC',
    'suppress_filters' => false,
) );
remove_filter( 'posts_clauses', 'wpse163696_posts_clauses', 10 );