I was honestly wondering because I have heard (on this board, particularly in a extensive "Reno cops" thread awhile back) is that, yes, you can refuse, but you'll probably be detained and the train will leave without you. While the cops may not have the authority themselves to put you off a train, the cops can and do ask the conductor, and he DOES have absolute authority to put you off, for any reason. You can complain to Amtrak after the fact and complain to the police agency after the fact, but in the meantime, your trip just got sideswiped.
I understand the thought, and at a traffic stop by all means, I would refuse a search, too, on general principle. The consequences would just be a delay in my daily life. However, on a train trip, in all honesty, I would probably submit to a search rather than having a trip ruined, which is a likely outcome.