Can the user see the shipping tracking number for their order?

PRESSERO > *Pressero FAQs

Tracking numbers can be entered on orders edited in the Pressero account, by going to the Shipping tab in the information windows for that order. The tracking number will be included as a clickable link in the notification that is sent to the customer when the order has been marked completed.
 
If the order itself has not yet been marked as completed, the customer will have the tracking number given to them in the email notification that goes out as soon as the order has been marked as completed. The customer will be able to select a live link of the tracking number in that email so they can track the package on the carriers site.
 
More detail on editing orders from your Pressero account, can be found in the Orders chapter of the Pressero documentation.