It's possible the immigration official will ask few questions and let you to go. However I would not prefer that route.
I had similar issue with photo page on passport started to come off, and I noticed 2 days before my travel back home, showed and discussed with a friend, we thought in terms of any travel, it is wiser to just go to any Indian Embassy get it fixed, or apply for replacement passport.
Went to Indian embassy, they verified my documents, and fixed the little tear in the passport.
Just imagine, if any immigration official dont allow you to travel, or just putting you for further inquiry may lead to missing your flight, or re-booking flights can cost you more than taking little extra caution to fix the passport.