We do have an option to enable this item to be received and fulfilled during order processing. (Service Item > Preferences > Can be Fulfilled/Received) However this Setup will not let Service Items to be printed in Printing Tickets/Packing Slips.
Workaround (Using Administrator Role):
1. Navigate to Setup > Accounting > Accounting Preferences tab.
2. Order Management tab > Picking/Packing portlet > and check Show Non-Inventory Items on Printed Forms
Try to print a Picking Ticket/ Packing Slip once again and check if Non-Inventory, such as Services or Discounts Items are already included.
Note: There is an Enhancement Request filed for this - 109026