I've done it! The first day in the great experiment of leaving the PC turned off is behind me, and it went pretty well. As expected, the battery in my iPad 2 has plenty of juice left even after a long day of use.
So far I haven't run into any major gotchas in using just the iPad 2, everything has been mostly as I expected. I was able to experiment with a few things that I've found difficult to do on the iPad in the past, and get around them with relative ease. As a result I have not had to resort to using one of the remote desktop methods for accessing a "real" computer from the iPad.
In no particular order here are the major observations of day one from using only the iPad for everything:
I used the iPad 2 in tablet mode most of the time, only using the keyboard for extended writing sessions. This led to me working far more comfortably than I normally do working at a desk all day. The work with the tablet can be done literally anywhere, and even using the keyboard it's easier to keep an ergonomic setup.
It's important to restate that I only use the keyboard for extended writing sessions. Commenters complaining that my test has me "carrying an extra piece (keyboard)" miss the fact the keyboard is rarely used, and becomes one with the iPad in the case when it is used. That is significant.
I worked in several venues over the course of the day, and I used the iPhone 4S to get the iPad online a couple of times. I believe Apple has done something to optimize iPad use with 3G on the iPhone 4S. It seems much faster than the speed tests show it to in fact be, quite noticeably so. I don't believe that's my imagination, it consistently felt like a fast connection when it wasn't.
I tested using the two remote desktop solutions with both the slower iPhone tethering method and the Verizon 4G LTE mobile hotspot. As I suspected might be the case, OnLive Desktop will not work over 3G; it fails to connect every time. LogMeIn not only connected fine over 3G, it worked rather well with the slow speeds. Both methods worked fine over 4G.
The first day went rather well, and while it is much too soon to conclude if this will work for an extended business trip I am feeling pretty good about it. I'll get into other details about how I am using the iPad for different things as I get further into the test. Meanwhile, happy computing no matter where you do it or what you use.