Indeed. While most airlines require bags to follow passengers' itineraries exactly, Amtrak has no such requirement. There are several places in the Amtrak system where you can check a bag from one place to another and--by design--the baggage goes a completely different route than the passenger or on a train running at a different time.

So, since Amtrak doesn't care when you're taking the train (within reason), you can show them your later-date ticket to your final destination and have them check the bags all the way through to there. They'll travel on the first available train to that destination and will then be waiting for you when you arrive.