Is Batou no longer "equipped" for a relationship?

As far as I'm aware Batou never pursues any relationships with women, that he's celibate.

In SAC celibacy, virginity, and men injured in war losing that part of themselves are constant themes. It appears to me it's also implied several times that Batou is on of them. That he got his first cybernetic implants beyond a cyberbrain as the result of such a war injury.

Is this established cannon, just implied, or just in my head. If it's cannon, or at least the thoughts of the creators, it would certainly explain his character more. Of course most of all why he never pursues Motoko.

Thoughts?