Hey,
The medium of education in Indian Institute of Managements in India is English. In fact, to crack the entrance examinations for MBA you need to have a decent knowledge about English. Plus, the interview and group discussion is in English. So, it's important to have command on the English language.
So, if you feel your English is not that strong, so start working on it. Read books and watch news and  try to write in English everyday. It will help you improve your English.
See, learning a language is a process. One learns every day. So, atleast learn to frame sentences so that you can atleast communiate and don't worry, about  anyone judging you. Just practice every day.
Hope this helps.
Good luck.

Dear Aspirant,

Communication is an important part when it comes to MBA as you have to give number of presentations that too in English

Its not a difficult part and you can improve when you practice more. So Yes, you can definitely survive in IIM as communication is not only part for survival in IIM

So MBA will help you to improve your English communication skills. Don't think as your weakness. Overcome it by practicing and learning more

Hope this helps