Actually US Customs has just started a new procedure on the Maple Leaf (the train from Toronto to NY City). If you are a US citizen or a Canadian citizen, then yes you will remain on board the train assuming that all your documents are in order.

However if your citizenship is anything other than US or Canadian, you will have to disembark the train and go into the building to clear customs. I believe that the new procedure will also require anyone doing that, to pay a fee for the processing to enter the US.

So far I've not heard of this procedure having spread to any other train. AFAIK, it is a pilot program that will be evaluated after 6 months. I think it's been running now for at least 2 months.