Can the Shipstation integration for Pressero pass the shipping cost back from Shipstation to an order in my account?

In most situations, you will be using integrated shipping methods on your Pressero site that will return a shipping cost at the time the order is placed into the shopping cart by a user on your site. The shipping cost of the order becomes part of the order data on Pressero and will be available in the site order history, the order email notifications, and in the order reports that can be generated. Using an integrated service like Shipstation can return the tracking number back on the order and close out the orders on Pressero.
Pressero also supports using non-integrated shipping methods on sites. A non-integrated shipping method does not produce a rate on the order placed on a site, so will show a zero shipping price unless a handling fee has been added to the non-integrated shipping method as setup in your Pressero account. A non-integrated shipping method does support assigning an Integration ID that can map that order to a shipping service on Shipstation. Please see the article Do orders using non-integrated shipping methods get pushed to ShipStation? for more information on setting up a non-integrated shipping method
But in situations where a non-integrated shipping method is mapped to a service on Shipstation, the order will not get the cost of the shipment from Shipstation. The order shipping amount for those orders will be zero, though they will get the tracking information posted back from Shipstation, and the order will be closed out when the order has shipped from Shipstation.
If you are considering adding the Shipstation integration to your account, please see Integration - ShipStation via Embedded Services for more information.