I can confidently say that not knowing Kannada when you start at NIE Mysore won't be a problem. However, if you still can't speak Kannada by the time you graduate, it might not look great for you. It's not a legal issue or anything serious, but it might come across as a lack of interest in the local culture, especially since this place will play a big part in shaping your future.
You'll definitely meet plenty of people in Mysore willing to help you learn Kannada. Four years is plenty of time to pick it up, especially since you might end up working in Bangalore.