Can a customer order without opening the website?
Yes. With Hibou the customer can send a design or pick a catalogue item, confirm size, quantity and address, and pay from a link, all inside WhatsApp. The store website does not have to be opened for that order. The brand's webstore still receives the order after payment.
From the THREADLY deployment
On THREADLY, customers in India finish custom and ready-made orders in the chat. The website remains the catalog and the order record. THREADLY's store record is WooCommerce. A THREADLY customer in the UAE is asked to check out on the website. That is a store rule for that destination, not a second product.