I took Amtrak home from Boston to San Francisco in 2007 after riding my bike from SF to Boston. Those 3 and one-half days on the train were harder on me physically than the previous 54 days on the bike. I rarely slept more than 2 hours a night, forgot to bring my own food onboard, and suffered on Amtrak snacks and microwaved hotdogs. The seats on Amtrak may seem comfortable to sit in, but try sitting in them for 84 hours straight or worse yet, try sleeping in them. I had to change trains twice, once in Albany, NY, and again in Chicago. Each time, there was a 2-3 layover wait. I experienced only "minor" delays, with the train getting into Martinez, CA only a couple of hours late. However, I think my experience is the exception rather than the rule. Longer delays should be expected. If you are going to do the Amtrak trip before you ride, I would suggest giving yourself a few days to recuperate before you start riding.
I shipped my bike home via UPS so I can't comment on using Amtrak to transport a bike. However, I saw how the Amtrak baggage handlers treated luggage, so I would make sure I had packed the bike very securely with a lot of padding material to increase the odds that your bike will arrive intact. UPS was a snap, although it costs some money. I just wheeled the bike into the local bike shop in Boston, told them where I wanted it shipped, they did a professional job disassembling the bike and packing it securely, and it arrived at my doorstep 1 week later without a scratch.