Have any BBA or BMS grads made it to IIM Ahmedabad?

Yes, there are a significant number of BBA or BMS graduates at IIM Ahmedabad. In fact, people from similar backgrounds can be found not only at IIM Ahmedabad but also at several other IIMs.

However, the truth is that Engineers make up the majority of the batch because they have an advantage in the Quant section of the CAT due to their background. There are people from all walks of life with degrees in the arts, business, and so on. Students from such backgrounds, including BBA, benefit from the diversity factor, which gives them an advantage in the selection process over Engineers if they have good academics and CAT scores. Therefore, you should begin working on improving your CAT scores.