The whole modern-day economy is customer-driven. Incidentally, as a soft skill trainer, I conduct training programmes on Customer Service Excellence ((even yesterday I conducted programme for a company in Bangalore) and also Internal Customer Service.
These days getting the first job is real tough. Grab any opportunity that comes in your way, irrespective of your education, degree etc etc. Try to learn anything and everything in your present job role and develop yourself.. It is very difficult, these days, to get the job you want, the job you desire in the first instance. As one of our friends have told above, you work on this job, learn the techniques and when you get the right opportunity you can move over.
However, if you start liking the job, who knows you may become an expert on customer support over a period of time. You MBA education will certainly of use to you in any role if you utilise your education in your job role.
Best wishes