An elastic agent will always have an 'Online' status, (i.e. 'Online' or 'Online (Disabled)'). If you disable an elastic agent, the elastic instance will remain online. However, if you shut down the elastic instance, then the elastic agents process is killed and will not appear in the remote agents list. Hence, an elastic agent will never have an 'Offline' status.
On this page:
To view your elastic agents:
Screenshot above: Elastic Agents