I don't know - "it could take months" surely wouldn't be shortly after launch. I hope Xbone can get its shit together though, I am thinking of taking a day off of work with some buddies to play some PS4/Xbone. I would be pissed if a broken OS/Online prevented me from playing some Killer Instinct.
This may be my interpretation of Famousmortimer's information but I think after the day one patch is installed you should be able to play Killer Instinct or whatever else. The party chat and online features being there and working is anyone's guess.
Again, that is what I am reasoning from his information but as long as the games work that is what matters first and foremost. I know some people won't be happy though. They'll be very, very upset if Live is not running smoothly.