Adding to italo's answer, you can also do this using jQuery.
function isEllipsisActive($jQueryObject) {
return ($jQueryObject.width() < $jQueryObject[0].scrollWidth);
}
Also, as Smoky pointed out, you may want to use jQuery outerWidth() instead of width().
function isEllipsisActive($jQueryObject) {
return ($jQueryObject.outerWidth() < $jQueryObject[0].scrollWidth);
}