Is it safe to `emerge -uavDN @world` while working? In a related question, a few answers ("Yes", "...no problem", "typically... no problem") verify that it is safe to perform `emerge -uavDN @world` while working. Is it really so (for Funtoo/Gentoo)?

Yes, this is fine and I routinely do this.

One thing to keep in mind for stability is when you see large updated to your DE (e.g. yesterdays addition of KDE 4.11.4) when the update is finished, logout/relogin just to make sure any DE programs you launch are in sync with the new libraries.