I think so... and you might not need the theater degree. First off starting a business is a very risky thing. Most of them fail. So the business degree would be very helpful. The intern/on the job experience will help you see that world from the inside. I'm not sure how helpful the theater degree is, it's less important you know design and more important that you really know what the gear is and how to use it. So again working in a business for a while seems really important. I think if it was me I would get the business degree and a job at a theater supply place, and
play community theater. Give that a few years.
Finally, in your business you need to surround yourself with people who really know their stuff. So making those connections in community theater and in the business will be really helpful to networking with people who you should consider hiring someday.
Of all the career threads, the one you are considering is the most risky, the one where our advice will help the least, and the most potential for failure with no
safety net. If you screw up as a board op, you just move on to another production... if you screw up your business you are in debt, out of work, and can't just move on to another theater. So that business degree, life experience, and the people you surround yourself with are critical. I would also seriously think about trying to find a business partner. Maybe someone who has the theater degree/years of experience but doesn't have the business degree.