$query = array( // ... your args here. 'count' => false, // 1. Don't set or set to false 'no_found_rows' => false, // 2. Set to false (default is true) 'number' => 5, // 3. Set to a non-zero value
);
$comment_query = new WP_Comment_Query( $query );
// total for the current results set, e.g. on page 1
$count = count( $comment_query->comments );
// total for all pages, same as when LIMIT is not set
$total = $comment_query->found_comments;