This is an undocumented feature, and is therefore subject to change without notice, however the infoWindow.close() method sets the map on the object to null (this is why infoWindow.open(map, [anchor]) requires that you pass in a Map), so you can check this property to tell if it is currently being displayed:
function isInfoWindowOpen(infoWindow){
var map = infoWindow.getMap();
return (map !== null && typeof map !== "undefined");
}
if (isInfoWindowOpen(infoWindow)){
// do something if it is open
} else {
// do something if it is closed
}
Update:
Another potentially useful way to write this is to add an isOpen() method to the InfoWindow prototype.
google.maps.InfoWindow.prototype.isOpen = function(){
var map = this.getMap();
return (map !== null && typeof map !== "undefined");
}