This is more of an NS Core question than a Patch Management question; however, I believe we do not support the Server Core OS. You may be able to install the agent on the OS, I haven't tested this, but I don't believe it is technically supported. Furthermore, Server 2012 is not yet fully supported either.
Additionally, the limitations for Windows Server 2012 are detailed on KM: DOC6193. This KM article is noted in the Support Matrix found on KM: HOWTO9965.
Hope this helps,
Joshua