When you run your code with Elevated Privileges, the code runs under the identity of the hosting application pool. SharePoint\System account exists ONLY within content of SharePoint runtime(not recognised by Windows Security subsystem) and map internally to the account under which application pool is running.
If you are running application pool under DOMAIN\SSUSER account, the code is still audited as running under SharePoint\System account. So, if you get access error on SharePoint site stating that SharePoint\System account don’t have access to the resource, this is because the application pool identity account don’t have access to the resource. Don’t spend time looking for SharePoint\System account :-)