As far as the popular food press is concerned, no. In fact there are more than a few recipe writers out there who will call an American-style layer cake a gâteau just so they can sound fancy. But in fact there are real differences between the two, even if the words themselves mean largely the same thing.
The main difference between cake and gâteau, at least to my mind, is in the layers. New Worlders, who’ve embraced chemical leaveners almost since the day they were invented, commonly make cakes with layers well over two inches in height. The classical, Old World cake making tradition eschews such theatrics in favor of egg foams. What results are cakes that are based on many thin layers, for the simple reason that even the mightiest egg foam can only heft a cake a short distance into the air. Indeed even champion génoise layers are but a handful of centimeters tall.
To compensate, most gâteau have thick layers of filling. These are frequently made of buttercream or fruit, and aren’t terribly sugary so as not to pummel the eater with sweetness. Thus in a gâteau, layers are almost a structural element, team players in the ensemble that is the finished pastry. New World cakes typically make the layers themselves the focus. Their ultra-sweet icings were originally meant to be a condiment, though in many circles they’ve become the cart that drives the horse.
One other distinguishing factor of a gâteau is that like its other Continental counterparts, its layers often contain some sort of nut meal, adding a level of complexity seldom found in New World cakes.