Yes, each IIM Ahmedabad batch profile includes many BBA and BMS graduates. In fact, you will find students from similar backgrounds in every IIM. But the majority of each branch comprises engineering students. Owing to their academic background, engineering students have an upper hand in the Quants section of CAT. 

Although the majority are engineers, you will find students from diverse backgrounds with degrees in Arts, Commerce, Science, etc. If you are a student of BBA, you will enjoy the diversity factor which will give you an advantage during the IIM Ahmedabad selection process.