Create a Search Form that only Searches with WooCommerce Sale Products

Yes, you can add search value in getting post query like this :

$args = array(
    'post_type'      => 'product',
    's' => 'search value',
    'meta_query'     => array(
        'relation' => 'OR',
        array( // Simple products type
            'key'           => '_sale_price',
            'value'         => 0,
            'compare'       => '>',
            'type'          => 'numeric'
        ),
        array( // Variable products type
            'key'           => '_min_variation_sale_price',
            'value'         => 0,
            'compare'       => '>',
            'type'          => 'numeric'
        )
    )
);

query_posts( $args );