A short answer to your question is yes and no
. An MBA will give you the theory, and classroom based practice in the skills you were mentioning. There are diverging schools of thought on this matter. Some believe that management, decision making, and leadership can't be taught, and has to be experienced; others believe that learning about it can equip you with a better foundation from which you make better choices. I personally feel it's a mix of both, with the edge going to experience. But that's just me, I'm more of learn-by-doing kind of guy.
You raised some interesting points regarding your situation. You mention you struggle to take on leadership roles due to your immigrant accent. Brother, that's the last thing you should be worried about, and that is the last thing that should be preventing you from taking leadership roles. My parents were immigrants, some of my friends and colleagues are immigrants, and let's face it, the B-schools that you and I will be attending will be full of immigrants. I can understand your hesitation perhaps based on the fact you're worried you might not be able to get your point across effectively, or your team might not understand you initially. In my humble opinion, if you strongly feel that you have the aptitude for your work and the task at hand, the only way to learn is to jump right in. You might be the worst leader the team's ever had, but I guarantee you that you will learn more about yourself and what your really need to improve on more than reading a textbook, discussing a case with classmates, or doing group presentations.
I can also understand the hesitancy to take on new roles at work for fear of messing up and not doing a dynamite job and having your job in jeopardy. But there are tons of ways to get leadership experience that doesn't affect your earning potential. Does your company have any organizations, clubs, or the like? How about out of work? Any churches, religious organizations, social networks (hobbies, etc) that you could join and take an authoritative role?
I've had alot of experience along the way, both academic and real world. I've also been in your shoes before, and I really feel that an MBA won't be a cure all for what you're describing. It will give you a better set of tools, yes, but you'll still have to get in there and 'build the fence' so to speak. Hopefully this helped, and Emory is a great program, I'm an alum (BBA)...and am looking at their MBA program as well.