I saw the CBP on my recent trip this past July coming home on the LSL at Utica. However, their inspection from what I could tell seemed very targeted; as in they had some info and were looking for someone in particular. And we didn't take much of a delay at all because of it.
This IMHO has seemed to be the case the last few years, that is to say, their visits are brief and apparently targeted when they happen. Contrast that to several years ago when the inspections were quite regular and took a long time and considerably delayed the trains. While of course it was never proven, and would probably be hard to prove without insider info, there were many in the press and the public (especially the riding public) who felt that the inspections were ordered by the very anti-Amtrak, anti-rail Bush administration to delay the trains and make riding more inconvenient and make the delays worse than they already were. After the media started picking up the story a lot, the inspections slowed down, went quicker when they happened, etc. This if memory serves started to happen during the final 2 years of the Bush administration and the trend has continued.
I'm not sure just how many were ever caught on the LSL, but there were several illegals caught on the Empire Builder over the years, including one rather high profile case. And inspections have caught many on the Pacific Surfliners coming up from San Diego. In fact, for many years that train seemed to be both a drug & illegal's run. It's not so much anymore to my knowledge, but still they continue inspections in order to ensure that the Pacific Surfliner's don't once again become a train for those avoiding the law.
My big issue with these inspections years ago was the huge delay incurred. 300 people were delayed for a hour or longer sometimes, just in the hope that they might catch one illegal. I'm of the mind that if they can't target someone specifically, then they either shouldn't be there, or if they want to go fishing then they need to board the train and stay on the train until the next station or some convenient crossing. Delaying 300 for a fishing expedition shouldn't be allowed IMHO.