Does Drew come from a privileged family?
It's certainly not true that you have to come from a privileged family to be a successful entrepreneur. Look at examples like Larry Ellison.
I lived with Drew through college and a bit after. The thing that grew into Dropbox was started in an apartment that I lived in while Drew and I were working at a different startup.
While I would say that I regret not being in the financial position to quit my job and help Drew out early on, I don't think he was able to do it because of his privilege. I also want to call out that I'm struggling justifying that last statement, because I know what a privilege being white, straight, and upper-middle class in America is. That privilege totally helped getting into MIT (by virtue of going to a good high school and so many other things). But, I'm pretty sure he didn't rely on his parents for cash. He probably just stole my leftovers out of the fridge. :)
The fact of the matter is that he's scrappy and smart. During college, we were both presented with an opportunity to make some side cash. Drew took more advantage of it than I did, and it was smart of him. He banked his own cash and lived cheap. Maybe he graduated with less debt than I did, and maybe that helped, but I think that would be the only leg up that he had.
It's basically our duty to take that risk.
Privilege is a fuzzy term. A lot of people are born into good families but achieve way less than what he has achieved. So his background would not matter much for his achievements but it might matter a bit in giving other people hope just the way whether Tim Cook is gay matters very little for him but it matters a lot to little gay kids who want to be like Tim Cook.