No, but not everyone is, or will be an American Millionaire, and if they were the American Millionaire will do something different to signal their wealth.

In Victorian times richer house holds had lots of knick knacks, they wore voluminous clothes. Clothes and knick knacks were expensive so they signified wealth. Through the 20th century these things got cheaper, so the rich went for other things to signify wealth, cars, travel, minimalism. Now we're at the point where the masses can afford those, so its 'experiences', au pairs and other things that require human labour, which is now relatively expensive.

All of this is a long winded way of saying that a millionaire lifestyle doesnt necessarily have to be high carbon. Just whatever is expensive/unattainable to the masses.