Is there any student with poor academic record who got into any of the top B schools like IIM, XLRI, FMS? PS - Non Engineer.

You can get the answer by yourself for this as B schools publish profiles of present students. Even a non-engineer with the same mark as you give you tough competition. All that matters is the value you add to the MBA class. I know someone who is a non-engineers and belongs to one of these institutes. Here is some of his experience. 

• He had conducted an annual fest in college with a budget of 7 lakhs and was also responsible for branding, fund collection, and social media marketing of the event.
• He worked as a media manager for 2 years and managed to upsell 20% from accounting media.
• He even had a small startup that taught young students skills of Radio Jockeying and stage presentation. Though he didn’t have much profit from it.

Now, from here you might have got some idea that how this he had loads of value to present in the B school rather than only marks. So, yes it is possible. Enhancing your profile does make lots of difference. All the best and think beyond marks as you aspire to be a business leader via an MBA.