Does the FedEx Ground Economy API support reference lines?

Yes, although they're not called reference lines in the API.

FedEx Ground Economy supports using the Shipment Options print_custom_1, print_custom_2, and print_custom_3 on a label. The maximum length of each can be 25 characters on the label. There is also room on the label for the Shipment Option invoice_number with a maximum length of 15 characters. You can read more about setting our Shipment Options in our documentation here.