Does it work with Square?

@envisiondesign

This option will only complete paid orders that call the woocommerce_payment_complete() / $order->payment_complete() methods. Most payment methods like PayPal and credit cards will all trigger this action.

Since shipping and access to the products shouldn’t happen until payment is received, orders that haven’t been paid won’t be automatically completed.

This means our plugin won’t automatically complete an order if your gateway is unable to recognize when a payment has been received.