Yes, I do know a friend who managed to get calls from many top B Schools despite having an average Undergraduate Score. Her profile looked like this

• 10th- 76%
• 12th- 68%
• UG- 64%

Although her marks witnessed a gradual decline, she was lucky enough to study at XLRI. Past academics are considered as one but not the major factors at XLRI, unlike IIMs that focus a lot on past academics. A good XAT and GD-PI score can compensate for your poor academic record at XLRI, FMS, and JBIMS. NITIE is a top B School that does not consider past academics at all. My friend with her average profile managed to convert NITIE, XIMB, and all the IIMs except for the top ones obviously. So we can safely assume that admission into these top B Schools is possible even with an average profile provided that you score excellently in the CAT or XAT and the GDPI round.