Yes, this is possible and actually a nice idea.
Basically create a simple widget, and remove the calls to comments_template() from other parts of your theme.
Example:
add_action( 'widgets_init', array ( 'T5_Current_Comments_Widget', 'register' ) );
class T5_Current_Comments_Widget extends WP_Widget
{
public function __construct()
{
parent::__construct( 't5_current_comments', 'Current Comments' );
}
public function widget( $args, $instance )
{
if ( ! is_singular() or post_password_required() )
return;
print '<style scoped>#commentform,#commentform *{max-width:100% !important}</style>';
comments_template();
if ( get_option( 'thread_comments' ) and comments_open( get_the_ID() ) )
wp_enqueue_script( 'comment-reply' );
}
public static function register()
{
register_widget( __CLASS__ );
}
}
Then drag this simple widget into a sidebar …

… and that’s all. You can read and write comments here now:

You should of course move the CSS to your real stylesheet.