Sure. Just like a BMW is a status symbol in a way that a Toyota Corolla is not. The irony in this case, which also applies to state vs ivy league schools, is that a Corolla is a more reliable car (cheaper to operate and cheaper to maintain too!) - so as a car it is 'better', though just not as 'cool'. Similarly, a state school will provide you a quality education at a fraction of the cost and afford you all or most of the same kinds of opportunities as a ivy league school.
So what does that mean for the 'American class system'? To me it means that we live in a a society where you can spend lots of money to acquire 'status'... or you can save that money and do your own thing.