Can I set up and use a Wii U without a separate display?

I don't own a TV or monitor, but I'm interested in a Wii U for games that can be played with only the controller.

Is it possible to go through all the initial console setup, downloading updates, etc, and then connecting to the e-shop to buy software using the Gamepad as my only display?

For the initial set up, you need to have a monitor to set the console up.

Even if you are done with the set up phase, depending on what type of games you play will determine if you can play it with just the pad or if it requires a monitor.

Games with the Off TV play is the feature that you are looking for.

List of off TV play http://en.wikipedia.org/wiki/Off-TV_Play

I recommend purchasing a tv monitor or a computer monitor if you plan on buying a WiiU console.