Will Updating Fulfillment Status to "No Fulfillment Required" Stop the Warehouse from Shipping the Package?

Updating the fulfillment status of an order to No Fulfillment Required will not send any cancellation to ShipCompliant or your warehouse. You will need to manually cancel the shipment with your warehouse to prevent it from shipping.
The status update simply updates it in Commerce7. 
If you need to cancel shipments, please set the order as No Fulfillment Required in Commerce7 and also reach out to your warehouse to stop the shipment.