Hi there,
Shopify supports a few different ways of integrating fulfilment services, first it is easy to create a simple custom fulfillment provider which will send emails to a certain address whenever something is to be fulfilled, this can be setup from your Shopify Admin. However what I think you are asking about is a bit more complicated but it is possible. You'll want to look at will be the FulfillmentService and the Fulfillment API in order to create an app for your fulfillment service. We created a bit of a template for doing this with ruby on rails here: https://github.com/Shopify/shipping-fulfillment-app.