It is possible to do this, just not with the API's insert function. You can write your own INSERT query instead. You always want to use the API when you can, but sometimes it's not possible. The query would look like this:
global $wpdb;
$wpdb->query( $wpdb->prepare("
INSERT INTO {$wpdb->posts}
VALUES( %d, %d, NOW(), %s, %s, %s, %s, %s, %s, %s, %s, %s, %s, %s, NOW(), %s, %s, %d, %s, %d, %s, %s, %d )",
$ID,
$post_author,
$post_date_gmt,
$post_content,
$post_title,
$post_excerpt,
$post_status,
$comment_status,
$ping_status,
$post_password,
$post_name,
$to_ping,
$pinged,
$post_modified_gmt,
$post_content_filtered,
$post_parent,
$guid,
$menu_order,
$post_type,
$post_mime_type,
$comment_count
) );
You'll have to make sure that the ID doesn't already exist in the database first. If the post table schema changes in the future you may need to update the query to account for the changes.