It seems that feeding the naga doesn't bring any positive benefits, and giving it all of myself doesn't have any special plot either.
It does have an effect and you should be able to see it on the side, with the other effects applied to you (can't remember how it's called).
It's however unclear how much is needed to progress to the next step. I don't know if the special skill is necessary or if any mean to make him grow works too.