I get the impression if your bike is boxed and checked baggage (with all that entails), Amtrak will transfer it on and off their Thruway coaches. Folder? You're probably good. Otherwise?
I've searched the Amtrak website and can't find a written policy for bikes and various journey permutations of train→bus→train. Maybe I'm missing something. Anyone? Bueller? Bueller?
While writing your senator or emailing your favorite cycle advocacy organization, see if you can get a favorable written policy on Amtrak Thruway buses + bikes.