Is it possible to add an alert that will notify you when a computer communicates with the core server? Looking at some Alerting documentation(8.8 although I am on v9 SP2), there appears to be a feature called device monitoring but this would hinder the core with it continuously pinging a long list of multiple computers.
Other than device monitoring which you've discounted, you could consider our State Notifier plug-in module. This adds real-time status updates to machines including the ability to be notified of a particular state change such as when a user logs into a machine or a mobile device comes back into the environment. Might be worth you taking a look. Links below.