You'll need the Internet to download, install and update Origin & SimCity, but you can play in Single Player mode, which is offline. I have a metered connection only, so I play offline. IIRC, the first time you open Single Player, it might throw an error wanting to connect to the Internet for Origin if you're offline, so enter the game and go into Single Player mode right after you install, just so it gets its first setup stuff done while you're still connected.
I suggest going through settings in Origin as well, I set mine to work offline most of the time, and disable things like sending usage stats to EA, etc.
