Yes, if you don't intend to play the character in a way that makes use of the status, this would be a disadvantage to your application.
However, making use of status isn't restricted to working in the family business. It is a matter of how the character was raised, how they live, what they think and what they believe. If being from a rich family does not affect how you play the character it likely won't get approved. However, I would need to see the application to say more.
Our comment whether or not the status is needed, however, had more to do with the fact that being "rich" is a matter of perspective. Some people applied for rich before because their char's family could afford food and books.