if "false !== WC()->cart->add_to_cart(...)" then the product has been added to the cart including persistence to the database however if "'publish' !== $product_status" then all subsequent execution including the response sent to the frontend of the program will be as if add to the cart operation has failed. The critical point is if "false !== WC()->cart->add_to_cart(..)" then the add to cart has succeeded and nothing should override this.
https://github.com/ClassicPress-plugins/classic-commerce/blob/10650f8347d4307b8b02ccdc76195e544cb50e51/includes/class-wc-ajax.php#L391
if "false !== WC()->cart->add_to_cart(...)" then the product has been added to the cart including persistence to the database however if "'publish' !== $product_status" then all subsequent execution including the response sent to the frontend of the program will be as if add to the cart operation has failed. The critical point is if "false !== WC()->cart->add_to_cart(..)" then the add to cart has succeeded and nothing should override this.