The brain damage all depends on how good of a boxer you are. If you don't want brain damage, you might wanna think about beefin up your skills before you enter the ring.

But to be a bit more serious, I'm no doctor, but any kind of trauma(e.g. getting slugged in the face) to the head can cause brain damage. While I don't think its GUARANTEED to give you brain damage, boxing can certainly be a step in the right direction towards hurting your brain.