I have checked a bagged Twenty on Amtrak as luggage before with no problems. Check the individual trains to make sure that there are no size restrictions, there are a couple (West Coast I think) that have smaller size restrictions. I have ridden Amtrak a lot south of DC down to GA, as well as up to the Philly area and west to Lancaster, and have never been questioned on bag size or number of bags, nor have I seen any one else questioned. All of the trains I have been on typically have overhead racks as well as luggage storage space at the ends of the cars. I love riding Amtrak, just wish they had faster travel times.
Aaron