Upgrading to OS X Mavericks (10.9) via Screen Sharing
I did this with absolutely no problems.

If you have Screen Sharing turned on in the Mac Mini then connect to it from another Mac (I used a MacBook Air) and save the password into the keychain on the 2nd Mac. You don't need ARD, normal screen sharing will do the job.

Now run the 10.9 installer. At the reboot you will lose your connection but just reconnect and you can watch parts of the install process. Then right at the end there is a final reboot and the Mac Mini is ready for you to reconnect again and go to work.

It's painless though I do admit to making sure I also had ssh set up and running before I did it "just in case".