I forget whether it was your team or someone else's team I was reading about, but isn't this the guy that does the live color commentary for the arena battles at the academy?
And if he isn't, does your A/V team include a battle color commentator?

You're correct, that's his main job with the A/V club, but all members of the team have the opportunity to do the occasional voice over or one screen segment. Not all do though.

Does he ever have the chance to do the color commentary live, right when the battle is happening?

Sure, if it's a big event.
Keep in mind, most of what the A/V club does is for the daily announcements. so that means commentary over edited pre-taped matches. But big school wide events would certainly get the live treatment. (I suspect they would even try yo swing a live video podcast from the pressbox.)

Really? So they'd only be seen commenting on the mid-term and final exam battles, and on any battles involving the top 5 overall teams in the school?

Anything the school would sell tickets for would probably have a live commentary.
Other event might have some pre-game interviews or more play-by-play coverage, but you've got to assume to a school that is centered around combat, there are going to be a lot of matches to cover.

Most days in the middle of the week I suspect you'll have something that's mostly a recap of the standings and a "best play of the day".