Still no wireless internet on most Amtrak trains
I say "still" because many busses, such as Bolt and Megabus, had wireless starting a few years ago (not totally reliable, but not bad). Amtrak has been slow. Wireless was tested on Acela trains starting a while ago, but Amtrak didn't have it going for real on all Acela trains until March 1 of this year.
As for other Amtrak trains? They say: "Amtrak is evaluating opportunities to implement Wi-Fi on other trains, but has no firm plans to do so in the near future."