How does CC handle Minecraft game exit?

I'm concerned that having a startup script that runs constantly might encounter problems when I exit my Minecraft world. I'm worried that it might interrupt the script and cause problems like variables or other data not being properly saved.

Is there any way for my CC script to detect shutdown, like an exit trap?

Nope. And computers will be freshly rebooted when loading the chunk they are in again.

So when leaving a chunk or exiting Minecraft it's possible for my script to be interrupted at any point of its execution?

That's correct. If a computer is not actively loaded either by chunk loaders or spawn loading, it will shut down as if you had held Ctrl+S.