You can't add a handler to the network link as there are no exposed events.
However you could simply set the time slider to the current system time every second to keep up with your Kml data.
// sets the current slider position to the current system time
function updateTime() {
ge.getTime().setTimePrimitive(ge.getTime().getSystemTime().getWhen().get());
}
var timer = setInterval(updateTime, 1000); //update the slider every second.
Obviously you could add other checks, to see if a particular element is present or if the slider is visible, etc.
If you need to stop the timer you would simply call
clearInterval(timer);