I know the OP now has a change in plans, but if there's no checked-in luggage, there's no need to check-in. You simply need your ticket and walk onto the train - either coach or business class. A lot of people don't bother checking in luggage on Amtrak because their carry-on size limits are about the size of airline check-in limits. On most routes, there's no problem as long as you get to the train before the doors close. Most people will have a self-printed e-Ticket these days, but there are several ways to display a ticket. Heck - most conductors will even look up a ticket by name if the passenger forgets it. I've done that when I had a ticket where nothing was legible except for my name and the route.
Amtrak's published requirement to check-in luggage is 45 minutes before the train departs, but I've heard final call announcements for luggage as late as 15 minutes before scheduled departure.