I would suspect that bikes could be accommodated in the bottom of an intercity type bus. I once took a bike from Quincy, IL to East Lansing. I bootlegged it in a soft case with strap as far as Battle Creek where it went in the bottom of a Throughway bus for the last leg. No problems.
I don't know how likely it is, but if they use a van to catch up with the Capitol Limited, you will probably wind up being put up overnight in Chicago because of the bike. This happened to us on a MSP - QCY trip; see
trip report. I understand your problem if they put you up overnight in Chicago, even if you aren't downgraded from sleeper to coach the next day. You would have to peddle extra hard to make up for the lost day.
PS. I've biked Cumberland to DC, Pittsburgh to DC, and most recently PGH to CUM, arriving and departing by train each time. I'm waiting for the Pinkerton Horn daylighting project to be finished before I go again. 5:03AM is early enough to be rousted out of bed to start the ride.
It is not considered politically correct to bicycle through the gap in the GAP near Pittsburgh. But if you are arriving in PGH by Amtrak, your only two choices are bike or bus from downtown to the Waterfront. If you are doing this next year, it should not be a problem since the last remaining gap in the trail is scheduled for completion this Fall. But in case it gets delayed, my trip report gives a routing from the
Amtrak Station to the Waterfront (actually to Duquesne since the Waterfront to Duquesne section had not been completed).
IMO the GAP is the best long distance trail in the country - well worth a train ride to get there.