Yes, there are many people who converted IIM, XLRI, FMS calls, even with a poor academic record. I personally know someone who scored less than 50 percentile in engineering yet got accepted at XLRI. He performed well in MBA and now works as a senior HR at a major eCommerce company.
Academic record isn’t the only thing that these institute takes into consideration while selecting students. Your entrance examination score, performance in GD-PI, extracurricular achievements, etc. are equally important.
One of my cousins got into XLRI without breaking much sweat and his story still continues to baffle me as getting into XLRI is not an easy job.
His CAT result was 81 percentile and his XAT result was 99.7 percentile. His XAT score earned him a call from XLRI. He did not perform well in his group discussion and personal interview due to his poor skills in public speaking. He failed to get any converts.
In his second attempt, he worked on the development of his soft skills.
As he had spent so much time honing his public speaking skills he did not get much time to prepare for his CAT/XAT which resulted in him underperforming.
In his final attempt, he studied without giving in to any distraction and also focused on his extra-curricular activities.
In the end, his CAT results were 99 percentile and XAT was 98 percentile. He managed to convert all his calls except one due to his now improved skills in public speaking. He has now completed his MBA.