It depends, doesn't it? Being wealthy doesn't mean that you're a nob, after all. And neither does a lack of wealth make you a nob. You become that by yourself, or with the help of an unhelpful enviroment.
Rich nobs tend to be the ivory tower-type, thinking poverty and bad things happen to people as a punishment for some lack of personal quality. Otherwise, they wouldn't be poor/ill/depressed, would they? It can't be too hard to stop being that, can it?
Poor nobs tend to be the type that thinks their personal hardship outweighs the needs and struggles of everyone else. Not everyone can afford a nice beach house, so why should they get one? Never done a proper day's work in their life, and everything wrong with my life is all their fault.
While people tend to only make friends in their own social class, since that is simply the most likely arenas where people meet each other, but if you do make friends on different parts of the ladder, I don't think there's any reason why you couldn't be friends.
It'll be more difficult. Some struggles will appear foreign, even a bit petty, to both parties. Some customs and expectations will be difficult, and it's difficult keeping a friendship running with vastly different lives and schedules. But with a deep enough kinship or common interest, it's entirely possible.