Hi,
I think getting an Indian MBA will helps in terms of getting hired faster. Most of the better business schools in India have bigger companies coming to campus for interviews. Having said that you should keep in mind that getting in to IIM-A or IIM-B is comparatively daunting task. CAT is not an easy exam, and what makes it even harder is number of people taking CAT every year.
I can think of one solution to this tricky situation. You can get an MBA from a school in US or Europe where they have joint degree/collaborative programs with IIM or ISB. I can't think of any name top of my head but I am sure ISB has joint degree programs. This way you will be able to participate in campus hiring on ISB or IIM.
About MBA from US.
Personally I would go for this option. There are several reasons for that.
1. Most of the American university degrees are recognized in India.
2. You can get a job in any international bank of financial institution and ask for a location in India
3. There are relatively less number of people asking for Indian job location than the whole demand.
I hope this helps. Let me know if you any specific questions. I know some people working in India after an MBA, they should be able to answer your questions.