NITIE Mumbai is the brand name for engineers targeting management courses in India. The institute offers various industrial management courses for students.
I have a friend studying PGDIM in NITIE Mumbai, and as per his insights, you do not get any advantage of being an Industrial Engineer in NITIE Mumbai, if you are focusing on PGDIM or PGDISEM. As it offers you an Industrial Management degree, having an Industrial Engineering does add anything to your profile. However, you may get an edge over other students if targeting M. Tech through the GATE exam.
Overall, in MBA from NITIE, an industrial engineer is on the same platform as other candidates.