There really isn't a clear cut answer. Depends on the individual circumstances of the applicant, business, timing, etc.
Quite a number of MBAs actually start businesses -- but the overwhelming majority don't do it right after b-school (the career reports for top schools usually have ranges from 1 - 5% of the class). However, if you were to poll alums 5+ years out of school, that number will be much higher-- maybe as high as 25%???. A lot of these businesses aren't high profile VC-funded companies (although some certainly are), but usually small businesses and self-employment.
Now, whether that MBA helped or not is debatable. Of course, if you want to be in the burgeoning multi-billion dollar industry of admissions consulting, then yes an MBA would help haha
Here's another way to look at it.
To start and run your own business, you need four things: BRAINS, GUTS, HEART and LUCK.
BRAINS: You need the brains (knowledge or know-how) - all the technical stuff like how to run basic numbers, do some business analysis, etc. Having more formal business knowledge like accounting, finance, marketing, etc. certainly is nice, but not necessary - in any case, what's more important is that you are able to build a team around you that has this knowledge. Some will say "but I need the finance knowledge" - NO. *You* don't, but you better make sure someone on your team does. In fact, as the company founder, you don't *really* need any formal business knowledge (because you can always hire folks with that knowledge - either as managers/employees or as contractors/consultants) -- but what you absolutely need that makes you the most important person in the company is SALESMANSHIP, VISION, and LEADERSHIP (none of which you'll learn in business school - but where you'll learn in the real world through experience). Think of some high profile founders - Michael Dell, Bill Gates, Steve Jobs, Larry Page/Sergey Brin, Pierre Omidar, etc. -- they were the linchpins not because they had business expertise - but that they were the Chief Hustlers or the main evangelists for their business - they are the face of the business, the head of sales (even if that's not their title), the ones that promote and brand the company. And then their ability to surround themselves with sharp business minds. Even folks like Jeff Bezos (finance - hedge fund guy) - Amazon wasn't successful because of his finance knowledge- it was his ability to hustle, to push/inspire his employees, to create a culture that encouraged experimentation, etc.
It's not about book knowledge you learn in a b-school. It's ultimately about real world leadership. Book knowledge is not irrelevant, but it's something that is nice to have.
GUTS: You need the guts (or balls) to get through some really rough and trying times - the willingness to face risks and endure big headaches along the way. And undoubtedly there will be.
HEART: You need the heart (passion) for the product or service you're selling. If you don't love what you do, it'll be that much harder to muster up the guts to get through the tough times (because the moment you face trouble, you'll more likely bail).
LUCK: And you need luck - being at the right place at the right time. Having the right product launch at a time in history where your customers are actually willing to pay money for it. Plenty of "ideas" are ahead of their time. Plenty are behind to the point where there's too much competition. And this sort of timing or choice of product/service isn't something you can calculate and manufacture (see heart and guts - if you believe in what you do, you will do it).
An MBA only gives you knowledge - you the individual has to bring the guts and heart, and your Divine Maker has to bring the luck.
A lot of businesses fail because of lack of knowledge. On the other hand, if you have an MBA and you start a business - its success or failure has less to do with lack of knowledge, and more to do with lack of heart or guts (i.e. overthinking, using "knowledge" as a substitute for judgment - otherwise known as analysis-paralysis, etc).
One last word about entrepreneurship. Most people (applicants) seem to view entrepreneurship as some solo journey. It's almost NEVER the case. A lot of businesses are founded by a team of people - because it takes the collective and complimentary knowledge of a team of people to make it grow and become successful. You can't possibly be the expert in everything, even if you are expected to do a bit of everything when running a business. As such, the "formal business knowledge" you may have is a luxury or nice-to-have, but not necessary at all so long as you have a team of people in place that do have that knowledge.
In other words, you don't *need* an MBA for yourself, because you can always hire one to work for you.
In fact, if you the entrepreneur/founder can bring the vision and leadership (the same sorts of things that CEOs do at larger companies), you can attract the right team of people to work for you who bring the specialized skills you lack (i.e. hiring and managing people that are smarter than you, whether they are PhDs, MBAs, MDs, engineers, etc).