I've seen a couple sites say that Amtrak has priority only when on time, and others that say it doesn't matter whether or not they are on time. None of the former that I've seen have provided a cite for the on time claim, though.
49 USC 24308 (c) says:
"Preference Over Freight Transportation. - Except in an emergency, intercity and commuter rail passenger transportation provided by or for Amtrak has preference over freight transportation in using a rail line, junction, or crossing unless the Board orders otherwise under this subsection. A rail carrier affected by this subsection may apply to the Board for relief. If the Board, after an opportunity for a hearing under section 553 of title 5, decides that preference for intercity and commuter rail passenger transportation materially will lessen the quality of freight transportation provided to shippers, the Board shall establish the rights of the carrier and Amtrak on reasonable terms."
49 USC 24308 (c) says:
"Preference Over Freight Transportation. - Except in an emergency, intercity and commuter rail passenger transportation provided by or for Amtrak has preference over freight transportation in using a rail line, junction, or crossing unless the Board orders otherwise under this subsection. A rail carrier affected by this subsection may apply to the Board for relief. If the Board, after an opportunity for a hearing under section 553 of title 5, decides that preference for intercity and commuter rail passenger transportation materially will lessen the quality of freight transportation provided to shippers, the Board shall establish the rights of the carrier and Amtrak on reasonable terms."