I use the Sprint version, but I believe the answer is the same.
Yes - you can root and leave TouchWiz the way it is.
Rooting this is almost as easy as rooting the GNex (at least on the Sprint version) - I'm guessing the same applies to the Verizon version too.
I didn't flash a new ROM, and didn't need a "trangle away" app (didn't even know about this app)
I don't know about the unrooting - there are videos that show how to do that, but I personally haven't tried it, so can't confirm.