No. I don't think they would have briefed them on a battle between Klingons and Romulans yet. It had nothing to do with their Vulcan rescue mission, as far as anybody knew. And their rescue mission was an emergency.
They weren't briefed on a battle that took place like 1 or 2 days before, of a battle of 1 Romulan ship against 47 Klingon ships, IN the Neutral Zone, but were immediately briefed on some earthquakes on Vulcan?
I can't agree with that logic.
Well, they monitored transmissions regarding a battle, versus receiving a distress call from a Federation member. It'd be like an India-Pakistan conflict versus Canada specifically requesting immediate assistance.