Does skipping "device enrollment" make files inaccesible to supervisor? Basically, I have a MacBook pro issued from work, I want to play some games so I have installed macOS X on external drive and boot from it. Now I get "device enrollment" notification every few hours and I always skip.

Does it make my files and traffic inaccessible to administrators? Or can they see whatever I am doing at a given moment on the device?
No, it doesn't mean that files, etc. are inaccessible to administrators as such.

When you have booted macOS from the external drive, and haven't enrolled, you're running the default software supplied by Apple alongside your own custom modifications.

However when you're booting from the built-in drive, you're running on an enrolled installation that potentially contains other configurations and software supplied by your employer.

If that software allows your employer to access external drives, then the file on your external drive are accessible by your employer. It is technically possible, but we cannot know whether or not your employer has installed such software.