I don't remember, I think it connected to the Internet to verify the Serial Key. It's not the Steam version so I don't think it connects to the internet to verify legitimacy every time I launch it. The back of the box doesn't say "Internet required to activate", just that I need a connection to play Multiplayer.

All the links that go to the GSC forums are broken. Only the FileFront ones work properly.

I found SoC had a few ... quirks.
Sometimes hostile NPCs (usually military or mercs) would wander into Duty territory. If you killed one, even in self-defense, Duty would flip out on you. You've got to run and hide behind some Duty guys, and let them handle it.
Some quest item locations are marked in the wrong spot on the map. The Duty soldier's rifle is marked in Dark Valley, when it's actually carried by a bandit in the Agroprom underground.

The only problem I had with CoP was NPCs would disappear. My guess is, the game unloads them to save memory when you get a certain distance away. The problem was, it wasn't reloading them quickly enough. If I hung around in a place long enough, guys would magically appear (hilarity ensues if I happened to be in hostile territory at the time). Strangely, that was solved by a no-disc crack.

Then you may well be able to do CoP vanilla. Aside from the one issue (which I think is pretty rare) I didn't encounter any problems. No broken quests, no unreachable items.

US retail version is disc check, no activation.

Like I said, the ONLY issue I had with SoC was with the one Duty quest. The guy's rifle was placed outside the transition border, so that every time I walked toward it, I would load the adjacent area, and the quest compass marker would point me in the opposite direction, back the way I came.