No , BBA students are not eligible for INET exam.  The selection is for sub-lieutenant officer in three branches:

1) Executive Branch.
2)Technical Branch.
3) Education Branch.

Now the educational qualification for these three posts are given below:

1) Executive Branch: In this branch you need to have BE/BTech with minimum 60% marks. The candidate must have 60% in aggregate in both 10 & 10+2. Also the candidate must have scored a minimum of 60% in English in the 10 & 10+2 exam.

2) Technical Branch: In this branch , one must have a BTech with a minimum of 60% marks.

3) Education Branch: A candidate with a first class in MSc is eligible.For some posts under this branch, BE/BTech students with 60% is required. The candidate must have 60% in aggregate as well as English in 10 & 10+2 exam.

For more info you can check Indian Navy career section.

I hope my answer helps you.  All the best for your future Endeavors!