IIM

The basic IIM eligibility criteria is graduation with at least 50% marks or equivalent CGPA (45% for SC, ST and PWD/DA category). Candidates appearing for the final year of Bachelors degree/equivalent qualification exam or awaiting their results, are also eligible to apply. In CAT exam, you have to score above 90 percentile.

Irrespective of all the qualifications you have, if you don't do truly that you are something passionate about, you are always left behind, do what you really want to do, but make sure that you have the right resources, planning and you are smart enough for it and success will come.

IIM Ahmedabad has 2 stages for shortlisting students:
Stage 1 : Students are shortlisted for WAT and PI round on the basis of a composite score which contains weight-age from students CAT score, Academic records and academic diversity.
Stage 2 : A final merit list is prepared on the basis of a final merit score which has a weightage from various parameters like CAT score, academic rating and performance in GD and PI round.

Please find the attached shortlisting criteria for the course.
https://www.iima.ac.in/c/document_library/get_file?uuid=3c0de5c2-5d78-4849-81ec-af4fd18863e3&groupId=187610&filename=Shortlisting Criteria for PGP 2020-22 batch
Now, technically it is fair to say that you are eligible, but some IIMs give more weightage to 10th and 12th. So, technically you are eligible. My suggestion would be to give your best efforts in CAT that should be the primary goal and leave the rest for afterwards once CAT gets over.

Yes, IIMs accept the GMAT score for admission to their Executive MBA programs.

As it is said "you should grab opportunity where you get". According to me, you should go for such a course if you can.

The minimum CAT percentile requirements along with sectional cutoff for IIM-A are given below for reference only.
1. PVRC : 70
2. PDILR : 70
3. PQA : 70
4. Over all CAT percentile : 80
For admission, your CAT percentile should be above 97. The academic performance is also an important factor and your 12th marks can be create some problems. However, the performance in What, PI and Entrance score can bridge this gap.