He probably is keeping an eye on the battle, sure. For one, to prepare himself, if he can, for when the Night King comes to him. Also, I'm sure anyone, anywhere, on that night would like to have known what was going on. He's sitting there, waiting for the ghouls to arrive, as the only one who can see what's going on elsewhere..... does he really have anything else to do?
As far as your contention that Arya couldn't have gotten past the dead, based on what happened in the library - she couldn't have fought her way through all of them, but (A) when she had her weapon, she easily killed dozens on the top of the wall, but in-close fighting with a mob of them for any length of time is a losing proposition for anyone, as Beric (and thousands of others) showed.
(B) But what the library DID show us is that she was able to make it from one end to the other, only feet or inches away from them, and even when they specifically looked where she was hiding just seconds before, she was gone, without a trace. If they don't already see her, in the open, she's very difficult to spot or track, apparently, as a faceless assassin might be expected to be.
I'm not sure how that demonstration of stealth where she actually gets past all the wights in the library and out the other end, matches up with your contention that it showed she would not have been able to get past the dead, especially with the Night King's focus so squarely on Bran.