Just thought I'd throw my humble opinion into the pot here - I see a big difference between whether or not you can parlay your education into a management position in the aviation industry and whether or not you'd be good at the job. I don't doubt one bit that with an MBA and throwing your resume at enough airlines that you could land an entry-level management position. But the bigger question is whether or not you'd be effective in the position - and this is where the aviation experience would serve you so well. In this day and age, aviation experience is sadly disregarded in the management ranks. Some years ago, for example, I was flying for a commercial carrier just coming out of bankruptcy and the new management that was brought in, rank and file, were all recruited from Frito Lay. Somewhere, somehow, the idea was planted that business was business and if these people could make a potato chip company profitable, then they could make an airline profitable as well. They were wrong. The management brought in, while highly educated and I'm sure compentent in the potato chip world, had zero aviation experience and it showed.
Anyway, I guess what I'm trying to say is that I would hope that you could find a way to gain some entry-level, worker-bee experience before you leap into management. It will make you more effective in your future management roles. You say you are over qualified for the CSR job - well, that would certainly be true if you didn't intend to move into management. Heck, there are plenty of things you can do to gain a working perspective of an airline....moonlight part-time as a baggage handler....or really go crazy and apply as a flight attendant....whatever it takes to learn about the daily operational challenges that employees face. You've already earned an MBA and a good understanding of business....now it's time to continue your "education" and gain an understanding of what it's like out on the line.
Best of luck to you in your endeavors!!