Accounting & Commerce

Yes, it is. There must be a clarity in your mind that you want to get into media or media related jobs. Mass comm. does not mean print and electronic media alone. Plenty of government jobs ask for masters in mass comm. Public relations officers and other profiles demand this. As you have a good base of account and commerce as well, it increases your prospects to claim jobs in financial domain or banking mass communication/PR jobs. And I believe, MA in mass comm. is safer than M.Sc. or other nomenclatures of this degree.
If you have decided, then do not avoid skill development during your master degree. From where you do it matters less, how you do it is actually important.

Eligibility criteria for CFA is as as follows:
(a) An international travel passport for identification and one of the following:
(b) Undergraduate education: A Bachelor's (or equivalent) degree or be in the final year of your Bachelor's degree program (you must have completed your Bachelor's degree program in order to register for the Level II exam).
Work experience: Four years of professional work experience (does not have to be investment related) or
a combination of professional work experience and education that totals at least four years (part-time positions do not qualify, and the four-year total must be accrued prior to enrollment).
As you are a graduate i.e BA economics, you are eligible to enroll for CFA.