I believe the current AnyDVD HD does indeed remove all the protection from HD-DVD movies, and I suppose that means you could copy it with Nero (Nero does support HD-DVD and Blu-Ray burning now, right?). However, that would be dependant on your having appropriate media... most HD-DVD movies released so far are on 30GB discs. I haven't seen any HD-DVD blanks (or burners, for that matter) in any store around my city so far, let alone dual-layer blanks. Besides, if there are any HD-DVD burners on the market, I highly doubt they're dual-layer.
Since I'm sure Nero doesn't yet include a Recode-type utility that can reauthor HD-DVD move structures or compress them to fit a single-layer HD-DVD, I don't think it will be possible to copy most titles at the current time.