The app won't help you with the more sophisticated features that Apple added this year (like shared notes) but that's okay. It would require far more tricky programming to do more than simply download content. And it does show you everything that is currently available via iTunes U (I double checked with my iPad).
Update: The app has been updated and it now works for me.
TBH, I'm not sure it can even download content. I've now tried it on a couple Android tablets (including my eeePad Transformer) and I cannot download anything. I can find the course pages, but when I click the button nothing happens.
Right now I'm scratching my head. This apparently worked for someone at some point, but it's clearly not working for me. What's more, I've looked through the various pages and I don't see where I can do anything to change it. (Perhaps the app doesn't like the latest version of Android?)
Even though I cannot get it to work, I'm posting this anyway. I'm hoping that it works for you and that someone might have pity on me and tell me how I can fix it. I am willing to put some work into troubleshooting my issues.
I definitely like the idea and I think the developer deserves a round of applause.