Yes, many students with backlogs have been admitted to IIM Bangalore. Here is a brief description of one such case in which the student passed the CAT on the first try but had one backlog from the seventh semester, i.e. the fourth year. The backlog and CAT were cleared on the second attempt.
According to the student, the interview was quite interesting and a little surprising to him, but if you are well prepared, it is not difficult to pass any exam. He was interviewed by the same panel that remembered him and the previous questions and answers. He was expecting a tough interview with difficult questions, but they let him off with great ease.
When it comes to freshers, IIM Bangalore prefers toppers. Even if an aspirant has a high CAT score, it is difficult for him/her to get a call from IIM Bangalore with a CGPA of less than 8.
For those with work experience and a good CAT score, they do consider aspirants having backlogs. One of my friends had a year drop and still managed to get an interview call with 99.78 percentile in CAT.
That being said, in the end, all that matters for final selection or conversion is your performance in the personal interview round.