A few years ago I worked out of the Reno crewbase and for whatever reason, #5 was almost 24 hours late coming through Nevada. The decision had already been made to turn the train at Reno and bus everybody on it to their remaining destinations in California so the equipment could depart on time that day as #6.

Some minor problem happened causing the train to stop for something and the next #5, running pretty much on time, finally caught up to it. The decision was made to let it pass and continue to run on time.

I thought it was a good decision. Why have two trains of pissed-off passengers when you could only have one?

So, yes, Amtrak trains have, indeed, been so late that they have been passed by the next day's train.