I just recently pre-ordered Fallout 4 for the Xbox One and I was just wondering if I will need to have internet connection to install the game. I know internet is required to get updates and patches, but do I need it to actually play the game. Any help would be appreciated.

No i dont belive you would need that. But it might be a day 1 patch. Who knows??

You shouldn't...though there will probably be a Day One patch like just about every other Xbox One game I've installed. I found what works best is to go to offline mode, install, then go back online and let it patch...saves a lot of time.

If I recall, you only need to have your X-Box One connected during the initial setup and when you install a game. The rest of the time, you can play offline. It's what I do.

Offline play was mentioned. It's why I assume the pip boy app with use local wifi, as opposed to talking to a server somewhere.

Considering there is a post from the devs at the top pf the page concerning Xbox One digital preorders and the need to re-install the game if you purchased prior to October 27, I would say the chances are high you might need internet to play successfully on Day One regardless of format.

Hopefully just patches, I like to travel with my console and I want to be able to play the newest patch offline.

I'm pretty sure for consoles it won't require any kind of activation. I look into this myself and found this:
Writing on Twitter, Hines stated the following: “PC requires activation on Steam. Console does not. Console ship on Blu-rays, PC ships on DVDs.”

He never did specify if consoles needed a patch for activation, all he said was they didn't require Steam so it's still pretty vague, but I think it's pretty safe to say consoles will be fine without Internet and the day one patch since for consoles the entire game is on disc.

You can read more about it here. No in game spoilers are in the link.
http://www.extremetech.com/gaming/216919-physical-copies-of-fallout-4-will-still-require-a-digital-download

I was under the impression that it was a requirement for the Xbox One that any game could be played without any form of internet connection. Unless of course it's one of those "MP" games, naturally.

Maybe when I get my copy of FO4 I'll unplug the network cable before installing and see what happens.