If a Betta fish's tail gets damaged will it die?

Nope...I touch my fish and he is still living! It also depends on the fish as to whether or not they will let you. I have my fish in my room, I see him every day, and talk to him. I knows me and trusts me and will actually come up if I put my finger in the water. On the other hand my bfs betta is in the dining room, and he is hardly ever home and never talks to it. It shunns away if you just put your finger on the glass near him!

I recommend building the relationship of trust up first.