Hye Rahul, Being straightforward that is not a good idea. As the opportunities you have are a bit less when compared to others and First thing being a Mechanical engineer you do not have much of ground work to enter into MBA Finance. And other thing is being Mechanical engineer you are familiar with hard work I think. Because MBA finance is a though one even for the one with commerce background. After all this, still if you want to go for it, I will assure you that the risk will pay off at end.
Good career & placement depends on the college you are pursuing MBA. If the college isn't the top one, then it could affect you to some extent. Your graduation & post graduatiuon will have no links in common, thats not a point to worry. At last what matters is what you wanna do in future.