I've done it. It's fairly straightforwards but the performance will be low. If all you want is a browser without any storage it will run fine.
One thing to be careful of is that it will mount your local hard drive, but it won't write to it unless you tell it to.
Just don't think it will let you browse anonymously. The only thing this gets you is protection from viruses being injected to your base system or any logging from your employer....
Oh, and btw, it's called Ubuntu.