Yes PayWhirl can be configured to send orders to Shopify. This depends on how you have your plan settings configured. When Shopify is connected to PayWhirl you will have these options in your plan builder:
The "Plan SKU" is passed with the orders to Shopify and can be picked up by a Fulfillment service such as ShipStation or Ordero.
The Place an order setting determines when the orders are sent out. There are 3 options:
Place an order when paid in full - Ideal for layaway type situations
Place on order on each installment - Orders are placed for each installment. This is the only option if you have installments set to "no limit"
Place an order on the first installment - Orders are only placed on the first installment.