Many months ago, someone asked specifically what size my folding bike will get down to, as they were considering buying one. I was not busy at the time so I dug it out to measure, if anyone is curious to see it folded, it is at:
folding bike versus road bike

That bike when folded is bigger than my Ritchey Breakaway when the frame is split. But my Ritchey (badged as a Raleigh) is not a folder, so I would be hesitant to try to take that on Amtrak.