Damn, I hate it when you ask a question in which I have to say something positive about Vince...
Assuming Vince wanted to be in the wrestling business, and didn't just grow up in it with the McMahon name already well-respected, yeah, Vince Jr would have gotten to the top anyway, even if he had to start from square one.
Vince is not a "genius" in any form or meaning of that word. What he is, is smart and driven to the point of obsession. He figured out ways to make money that his father and other promoters either didn't think of, or didn't follow through with. Vince didn't invent merchandising, that had been around for decades before he came along. But Vince exploited it to it's fullest degree, putting the WWF/E logo on EVERYTHING along with various wrestler's names and likenesses, and sold them, creating a steady income-stream that does not stop. Vince has a knack for marketing, he IS good at that, able to market just about anybody as the greatest thing in the world, getting large amounts of people interested enough to pay to see him. So, basically, Vince didn't NEED his family's money, he would have made his own. The family fortune just helped him get to the top faster.
Vince's work days are legendary. The man never seems to stop working. He has the drive that all business tycoons and self-made millionaires have, from Bill Gates to Donald Trump. Vince is just like them. His single-minded goal to become the largest and most powerful promoter in the business became his life's goal, his obsession, and he did EVERYTHING he had to, dirty or not, to accomplish that. Even after wiping out all of his competition and achieving his goal of ruling the wrestling world (in North America, anyway) he still doesn't stop. His drive won't let him.
Family fortune or not, Vince would have eventually reached the level he's at now. His intelligence and drive got him there. The family fortune just helped get him there a little quicker.