It probably does. I don't have Kerbal, but I've seen in other Unity games (Unity 5 more exactly) the analytics files it creates every time a game is running. You can easily end up with hundreds of small files and folders. And it tries to connect to the internet.

Here's a blog from Windward's developers confirming that Unity collects some anonymous statistics about hardware. Windward is made with Unity 4, I think, and it doesn't create those analytics files, but it tried to reach the internet first time I launched it. As I don't play multiplayer, I block all the games in the firewall.

The Unity 5 games will create their config, analytics and save files inside the folder:
C:\Users\*user name*\AppData\LocalLow\*company or dev's name*\*game's name*\

Here can be a bunch of folders and/or files, but what you need to look for is the Unity folder, which keeps the analytics files, so you'll see something like this:
\Unity\*big string of letters and numbers*\Analytics\ArchivedEvents\

Inside the ArchivedEvents folder are lots of other folders which contain 2 small files, e and s. You can safely delete everything in this folder. Those 2 small files can be viewed with a text editor, like Notepad.

The Signal From Tolva is a Unity 5 game that I played recently and testing it today, it tried to reach IP 52.85.184.163, an Amazon cloudfront.net server.

I personally make a custom entry in CCleaner for every game that makes this crap. People who don't know about this, will probably have thousands of these files and folders. Or maybe they get deleted after are sent to those servers? Don't know, I won't give it internet access to test it. So it wasn't enough that many Unity games run like crap, now they're filling our drives with telemetry junk.