No they didn't.
Hilary was braindead, lazy, vain, college drop out that wasted her life and some how eventually made it to be a talk show host.
Carlton was confused for most of the show, a compulsive and stumbled his way into Princeton thinking he should be a damn bowler.
Will goes to college after like doing nothing besides chilling the entire series.
Ashley stumbles and bumbles around becomes a singer and model, rather unsuccessful though. then enrolls into a performing arts school
If your parents are multi-millionaires and you are this aimless in life, your parents failed you. Think about it, even the Cosby Kids ended up worst off than their parents.
You never see any of these kids achieve type of success through like hardwork and determination, achieve through privilege of being rich. They are aimless, drifting through life, their parents not really giving them a path to success. They are just there. Only people wtih any type of personality that is worth a damn is William and Ashley. Will wasn't raised by them. Ashley rebels against them. Hilary and Carlton were completely and totally snobby and repulsive human beings until Will came around.
It was a good show, but these were some shitty ass parents at developing their kids to be better than they were. Will was the one that made Hilary and Carlton better people, but they even let him fail lol.
And lets not even talk about the Cosby Show, all their kids were fucked up.