The answer is a Big “No”, if you are an Indian Citizen.
But in case if you are an foreign Citizen travelling within India from one airport to another then Passport of your country is necessary as it is being used to verify your Photo Identification as well as Verification at the entry point of Airport and before boarding the plane at the Check-in counter.
If you had Web-Checkin then you can directly walk-in without going to check-in counter!