That's a good guess. You you should be able to carry the boxed trailer on board if it meets the size requirements for carry on luggage. I was just in Penn Station (NY) yesterday and saw the test fitter, butI cannot recall the size limits for carry on.

If it's too big to carry on, you will have to check it. Not all trains have checked baggage service. For trains that do, as noted above you can only check and retrieve baggage at stations that have checked baggage service. In other words, your train must have checked baggage service and your origin and destination stations must have checked baggage service.

With all this said, some Amtrak trains have roll-on bike service. I cannot tell you whether such trains can/will accomodate fully assembled trailers.