Dee, single bikes are very easy but I'm not sure tandems can be accommodated in the same vertical racks (a bit too short). Amtrak says something about this on the Capitol Corridor line website. HOWEVER, sometimes the conductors are lenient about things if you are riding on non-peak hours. I've never seen a tandem on Amtrak except boxed as baggage but I have seen other bikes with fenders and stuff that wouldn't work in the rack but only at non-peak hours.
I would recommend that you join and post to the Davis Bike Club mailing list. There are a lot of people who use Amtrak as part of a commute or part of recreational rides. I bet some someone on that list will have direct experience.
http://dbclist.org/mailman/listinfo/dbc