Yes! BBA is also eligible for UPSC or any other civil service examination. See the point is, no degree is at all helpful for any government examination. Its the preparation of the student and how much he/she have practiced matters the most. So if you practice good for the government then only you can pass the examination with good rank.

To know more about Government Job exams you may visit the link below:

https://competition.careers360.com/articles/government-jobs

I hope this answer helps. All the very best for your future endeavors!