No, the carrier does not have registration or reporting duties as long as taxes were assessed (in the case of highway fuel) or dye was added (in the case of NRLM) at the terminal.
There are recordkeeping and PTD requirements, however. These requirements are listed in detail in §§ 80.590 and 80.592 of the regulations.
Questions and Answers on the Clean Diesel Fuel Rules (PDF)(135 pp, 888 K, EPA420-B-06-010, July 2006, About PDF)