Short answer: no!
I took the train from Chicago going to and from New Orleans to attend AGU 2021, and experienced a 6-hour and a 3-hour delay, respectively. Given that there was a tornado that ploughed through the train route, I wasn’t too bothered about it. But I’ve heard several complaints about Amtrak being always late, so I wanted to check the data and see for myself. This analysis is also inspired by a tweet from @douglas_rao https://twitter.com/douglas_rao/status/1469863061494272001
I downloaded 10 years of reported data from https://juckins.net/amtrak_status/archive/html/home.php and explored around. Full analysis can be found here.
Based on the histogram of arrival delays, it looks like my experience is on the extreme side, and that it is more likely for the train to be on-time, or be within an hour of scheduled arrival.
The histogram below shows that despite delays arriving at the other stations along the route, the train is almost always able to make up for lost time and arrive in New Orleans on-time or earlier than scheduled.
The same thing can be said for the trip back from New Orleans to Chicago:
Comparing arrival times at the Chicago Union Station against the other stations, it looks like the train arrives within an hour of schedule most of the time.
Overall it seems like trains are more likely to arrive on-time than have delays, and if there are delays it would be just about 30 minutes or less.
There is clearly room for improvement, and definitely not comparable to the reliability and speed of the train systems in many other countries, but it is still a reasonable alternative to driving or flying.