Advantages of doing an MBA after CA
First, and most importantly, the decision to prepare for CAT and go for an MBA after CA will depend on which domain you are interested in and want to work in. If the traditional areas of a CA (Accounting, Auditing, Corporate Law, Taxation), are what interest you, then there would hardly be any value addition in doing an MBA.
On the other hand, if you want to make a career in Finance (read: enjoyed studying SFM in CA Final), doing an MBA makes a lot more sense. As a CA+MBA, you will have more chances of breaking into niche Finance related domains like Investment Banking, Corporate Finance, Private Equity, Consulting, etc. (There are a bunch of roles in Finance, post-MBA. Just do some web research and you'll know).
Secondly, as a CA, joining a B-school will only be worth it, if that B-school is among the top 10 or 15. Otherwise, it won't add much value. Target IIM-A,B,C,L,I,K; XLRI, FMS-Delhi, JBIMS, SP Jain, IIFT. These B-schools should be given top preference.
So, at the end of the day, you will have to do a bit of introspection about what you want to make a career in. For now, it would be best to get a job, or continue working if you already are , and prepare for CAT alongside if you do decide to have a go at it.