Change link to other post to shortlink in the editor

The links in that dialog are made by wp_ajax_wp_link_ajax() (see wp-admin/includes/ajax-actions.php, there is no page on Codex or queryposts.com for that function).

To change the links filter 'page_link', 'post_type_link', 'post_link' and maybe 'attachment_link' after check_ajax_referer() was called for the action 'internal-linking'.

Okay, sounds a little bit complicated, but it is really easy. 🙂
Plugin on GitHub: https://gist.github.com/3731739

add_action( 'check_ajax_referer', 't5_temporary_internal_links', 10, 1 );

/**
 * Turn permalinks into dynamic links.
 *
 * @param   string $action_or_link Action when called per 'check_ajax_referer',
 *                                later the permalink.
 * @param   object|integer $post
 * @wp-hook check_ajax_referer
 * @wp-hook page_link
 * @wp-hook attachment_link
 * @wp-hook post_type_link
 * @wp-hook post_link
 * @since   2012.09.16
 * @return  string
 */
function t5_temporary_internal_links( $action_or_link, $post = 0 )
{
    if ( 'check_ajax_referer' === current_filter()
        and 'internal-linking' === $action_or_link
    )
    {
        add_filter( 'page_link',       __FUNCTION__, 10, 2 );
        // You cannot search for attachments in this dialog,
        // but a plugin might have changed that, so …
        add_filter( 'attachment_link', __FUNCTION__, 10, 2 );
        add_filter( 'post_type_link',  __FUNCTION__, 10, 2 );
        add_filter( 'post_link',       __FUNCTION__, 10, 2 );
        return;
    }

    $id = is_object( $post ) ? $post->ID : $post;
    return home_url( "?p=$id" );
}

But … when you change permalinks you have to create redirects in a server configuration file anyway to redirect existing URLs. So I am not sure if this plugin is really needed.