No, DO NOT OPEN the box before giving Wii U as a christmas present. People can handle that install time, getting what's practically a second hand / used console is a much, much, MUCH worse alternative. I don't think I would even accept that gift. I know for sure wouldn't be able to enjoy it.
This strikes me as somewhat OCD. Fair enough - if youre buying electronics for a regular user, let them deal with it. If youre buying for kids, why not set it up ready to go. Kids would much rather be in and playing a new mario game or whatever rather than watching a menu bar do nothing for two hours while millions of other consoles are clogging up the servers on christmas morning.