I took the CZ in March, with an AT&T iPad, and a Verizon iPhone. This is what I found:
Most of the route does have service, although strength and signal can vary heavily. All of the carriers struggle in Colorado, and specifically the Rockies. I remember not having a solid signal for a few hours while we were going through the mountains, but since that is the most scenic part, it shouldn't be a big deal. AT&T also tends to roam quite frequently while going through Nevada, although if I remember correctly, it should be 3G for the most part (make sure that data roaming is enabled within your phone's settings, in order to take advantage of it). They don't charge extra for roaming, but may take issue if you use tons of data off-network (shouldn't be a problem though, since the Nevada portion is mostly at night).
Besides the Rockies, you shouldn't have any major problems, at least along the CZ portion of your trip. I haven't been on the SWC, or the CS, so I can't speak to the service on those routes. I can infer though that service along the CS portions should be relatively good, since Amtrak does offer WiFi in the Pacific Parlour Car (which first class passengers have exclusive access to).
If you have an iPhone, I'd recommend downloading an app called Coverage?, which gives you a map of each carrier's coverage throughout the US. It does cost a few dollars, but I've found it to be invaluable. It will show your location using GPS, so you'll know when you're about to enter an area with bad/no service.
