Embed ‘New Post’ Form Inside ‘New Post’ Form

Yes, it is possible to hook into save_post action of one post type and do a wp_insert_post in the other post type.

Notes:

• the Meta Box is only generated when a new post is being created.
• the post types involved are portfolio and gallery.
• the meta box appears in portfolio and contains only one textarea field that is used for the content of the auto generated gallery post.
• the title of the auto generated post is the same as the original post.
• adjust for the proper post types.
• add fields as required.
• adjust the post array $add_cpt_clone as required.
• use $p_id to add tags (or custom taxonomy) to the auto-generated post. Refer to this Answer to see how to.

add_action( 'add_meta_boxes', 'add_custom_box_wpse_76945' );
add_action( 'save_post', 'save_postdata_wpse_76945', 10, 2 );

/**
 * Meta box for PORTFOLIO post type
 */
function add_custom_box_wpse_76945() 
{
    // Show ONLY when creating a NEW POST
    global $pagenow;
    if( 'post-new.php' != $pagenow )
        return;

    // Add meta box to PORTFOLIO    
    add_meta_box( 
        'sectionid_wpse_76945',
        __( 'Create Post in another CPT' ),
        'inner_custom_box_wpse_76945',
        'portfolio' 
    );
}

/**
 * Meta box content 
 */
function inner_custom_box_wpse_76945( $post ) 
{
    // Use nonce for verification
    wp_nonce_field( plugin_basename( __FILE__ ), 'noncename_wpse_76945' );

    // Field for data entry
    echo '<h4>THE_CONTENT</h4>';
    echo '<textarea id="the_content_wpse_76945" name="the_content_wpse_76945" cols="90" rows="5"></textarea>';
}   

/**
 * Creates a new post in GALLERY post type
 */
function save_postdata_wpse_76945( $post_id, $post_object ) 
{
    // Auto save?
    if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE )  
        return;

    // Correct post_type
    if ( 'portfolio' != $post_object->post_type )
        return;

    // Security
    if ( 
        !isset($_POST['noncename_wpse_76945']) 
        || !wp_verify_nonce( $_POST['noncename_wpse_76945'], plugin_basename( __FILE__ ) ) 
        )
        return;

    // Prepare contents
    $add_cpt_clone = array(
                    'post_title'   => $post_object->post_title,
                    'post_content' => $_POST['the_content_wpse_76945'],
                    'post_status'  => 'publish',
                    'post_type'    => 'gallery'
                  );

    // Insert the post into the database
    $p_id = wp_insert_post( $add_cpt_clone );

    // Use $p_id to insert new terms
}