You are certainly at an interesting cross-roads. I was essentially in the same position as you about 15 years ago, and have since gone on to finish a masters, work as a software engineering manager, and to work as start-up employee and founder (my current endeavor).
First, I think there can be some misconceptions about what an advanced degree will do for your career, whether your goal is to be an engineering manager or start-up founder. In particular, while many start-up founders and engineering managers have advanced degrees, the advanced degree in itself is neither a sufficient or necessary condition to ascend to or be successful in these roles. For example, without some real world experience to compliment an advanced degree, I think its unreasonable to expect a promotion into an engineering management position. Similarly, there are many successful engineering managers without an advanced degree; however, some/many large companies admittedly make this a key requirement.
Some would think ascending into an engineering management role (or start-up founder role, for that matter), will progress their career and make them happier and more successful individuals. After all, compared with being an individual contributor engineer/programmer, this is seemingly a step up in job title, responsibility, influence in a company, etc. I personally know several people who became engineering managers, but found they were absolutely miserable with the day to day responsibilities of project planning, personnel management, writing status reports, attending meetings, etc. I personally enjoy all these things, but your experience may differ.
On balance, I think "working your way up" ultimately holds more promise to becoming a successful engineering manager than an advanced degree (also see Steve Meier's answer). For me, "working your way up" meant showing a sincere interest towards management oriented tasks, even while I was still an individual contributor engineer; for example, this included writing specs, formulating estimates, helping with project planning, attending customer/marketing meetings at every opportunity, and taking on technical lead responsibilities.
Despite my comments above, I wouldn't necessarily dissuade you from pursuing an advanced degree. For me, finishing a masters has had numerous other benefits, such as becoming a better writer, increasing my ability to independently research and analyze advanced topics, and further exposing me to the academic underpinnings of software engineering. However, I don't think it has had a primary impact on my success (or lack thereof) as an engineering manager or startup founder.