If the tickets have not yet been paid for, you can pick them up at any staffed Amtrak station or QuikTrak machine prior to the ticketing deadline. If the tickets have already been paid for, you should be able to pick them up at any staffed Amtrak station or QuikTrak machine at least up to the departure time at the originating station on the itinerary. Check on the Amtrak website (under "Stations") for hours when the ticket window and/or QuikTrak machine will be open at the station where you wish to pick up your ticket.

You should not have any problem boarding at a station between your ticketed origin and destination, as long as the ticket is for the particular train you are trying to board (as opposed to an earlier or later train).