Of course, but think of all the rich kids and trust fund babies that end up doing nothing useful with their lifes. I think Gates family background was incredibly useful in his career (as is usually the case with most entrepreneurs) but still decided to do things that were out of the comfort zone for a kid in his situation. Most of the other kids would have opted to follow a career in finance or law and use his family name and connections to carve a comfortable "successful-in-appearence" professional life.
Wealth is not as great a motivator as we tend to think. Social and family expectations are much more important, especially in rich and upper middle class families, in determining what to do with your life. Gates took and odd bet. He could because the stakes weren't that high thanks to family money, and it paid off.