Yes you are eligible  for giving CAT exam.  When you get a good CAT score and during interview round , it will be asked about your 1.5 year extended duration of study reason. If you can provide them with a good logical answer and have a good academic and CAT score, I dont think you will have a problem getting into IIMs. But it will all depend on how you perform. 

You are absolutely eligible to sit for the CAT examination if you have a minimum of 50 % in graduation. Just try to score more in CAT examination and then you can easily convince the interview board to select you. 

If you manage to get 97+ percentile then you can easily go about saying that you've worked on yourself and that's why you got such good scores. If you perform well in the GD/PI rounds your justification will be genuine. 

All the very best