The short answer: "No, hell no, unless you've lived under a rock for your entire young adult life and somehow managed to fool adcoms with your people's skills and common sense practice which you clearly lack."
The long answer: an MBA is the modern day, irrelevant professional degree for someone who lacks any real-world experience with people, financing, or business strategy for growth. Truth be told, people who become millionaires holding an MBA are generally older-generation business-starting politicians or family businesses that would've ended up being millionaires anyway. So here's an MBA 101 gameplan for you in dentistry based on people who've actually worked as a young adult:
1. Buy as many finance and general business books to learn principles on different concepts. Make it a commitment not to spend more than a small amount for material.
2. Learn how to properly brand, market, and advertise yourself and your business. Brand is everything in a growing saturation of dentists in high population areas.
3. Be a good boss to your staff, and be good with people when you service them. If you need to buy more material, learn about the strength of business psychology and why people tend to "buy in" to certain businesses more than others.
4. Never be dishonest or non-transparent in your business dealings as a dentist to patient. It will hurt you long-term. That doesn't mean you need to under-charge, and you should certainly search for ways to bring in more revenue over a period, but don't overdo it.
5. Learn from dentists in your region for free who are successful in dentistry with respect to franchising or lucrative single-practice clinics. Soak up as much you can. Not everyone who is rich in medicine/dentistry is unwilling to help someone else.
6. If you absolutely want to spend some money on education, go for a Lean Six Sigma Certification up to a Black Belt, which teaches you how the ways to succeed in operations, workflow, and other dental-related ideas that are related to being successful in this field when you're first starting out. Plus, it's much cheaper to do.
Honestly, increasing the value of your service and brand as a dentist is directly related to your ability to produce quality work that people keep coming back for... so do well in your DMD/DDS to develop your knowledge and handskills.
If you can earn an MBA for free concurrent with your degree and you feel you can handle the extra coursework, go ahead and do it. Don't shell out another $100,000 for some extra letters that will most likely not tangibly change who you are as a businessman. Generally people are who they are by their mid-20s based on personality, work ethic, and drive to succeed. An MBA won't give you that spark.