In ePO you can set, in the agent policy, to display the agent icon in the system tray. In this case, the icon won't show until the agent checks-in to ePO and pulls the new policy.
Machines should not become unmanaged if once managed. So, you shouldn't have to worry about relying on your users to verify for you.
You can also add the following monitor to the dashboard: MA: Agent Communication Summary. That will show you machines that are checking-in and compliant or machines that have stopped communicating.
Depending on the number of client-nodes you are managing, you will likely want to troubleshoot why agent are failing to update and get it fixed rather than find another way which may be more administratve overhead in the end.