No. In general it is actually best practice to not have a LANDESK agent on your Core Server. You can run all actions you need from the LDLogon folder.
Frank is correct, you don't need a SP2 Agent before upgrading the Core.
Sorry, but perhaps I did not word my question properly. I've already installed the LDMS 9.6 Core (a side-by-side upgrade from 9.5) and applied the "LD9.6 Core SP2" to it. By the way, both installation files (LD9.6 Core and LD96 SP2 Core) are self-contained extractors and once extracted, the Setup.exe is run from the respective folders. There was no issue with the process. The reason I mentioned this is because the "LANDEDK960-SP2-Cient.exe" also appear to be a self-contained extractor. Which leads me to believe that it too, will have to be run on the Core. Perhaps its updating some agent files or something - I'm not sure. I wouldn't think that the extraction would take place on the individual clients. But, I could be wrong.
At any rate. I'm not clear as to what the documentation is saying and need clarification on how to get the clients updated with SP2.
NO, the client.exe is used to update the agent software installed on your managed devices from base 9.6 to SP2. You can use this a Distribution package, but you can also download it via Patch Manager and deploy through there. All the files in the client.exe are included in the core.exe, so any new agent you deploy after installing the core.exe will contain the SP2 files.
so, to summarize:
the core.exe needs to be installed on the LANDESK Core Server
the console.exe needs to be installed on every computer you have the LANDESK Remote Console installed
the client.exe needs to be installed on every managed device, or you push new agents out after installing the core.exe