It's highly unlikely you will be able to do anything else when an actual update is downloading and installing. No console so far has allowed that and the Wii U will be no exception. Even phones and tablets don't allow you to do that. However downloading games, demos and DLC should allow you to do other things on the console unless the console is designed to suspend downloads when this is done due to resource issues.
Im just talking about downloading. Windows ,mac, android and some other stuff. lets you download the updates while doing other stuff.
Yes i know its impossible to do stuff while the system is installing the update. But to just download the update it should matter.