This guide explicitly says that Core is supported on 2008 and not on 2016. How about 2012 r2? I have many 2012 r2 running Core with HyperV and I cannot patch them.
Agentless scans and deployments work on 2012 R2 Core, I'll get the PDF corrected.
What scan error do you receive? Troubleshooting Shavlik Protect Patch Scan Error Messages
What output do you see when running this from a command prompt on the 2012 R2 Core server? systeminfo | findstr OS
Retrieving data ...