You dont need to know the score in the way that coaches, players, and fans do - but it is an aspect of the game that is at times part of umpire a) duties and b) good officiating.
We are responsible for enforcing Run Rules and game ending run situations. We need to know tie games. It is important you understand certain game situations as part of umpiring and being a student of the game. Most often as PU, I keep track of the runs as part of what I do between innings.
It is not a sin to talk to people involved in this game and the level of play (championship/tournament/friendly) may determine how you must approach that. If its a regular joe tourney I may ask the book to run and grab me a cup of coffee in between padding her kids stats. I wouldnt do that in championship play
If you do need to talk to the book - talk to the book.
What you CANT do is something horrible like I saw a few weeks back.
Umpire loses count.. goes to the book
Book says count is 2-2. Other team is complaining the count is 2-1. He says "We gotta go by the home book - home book says its 2-2, so its 2-2". They say, well they arent the home book, we are. Ump says, "ok counts 2-1".
Meanwhile, he never did go to his partner. That was so bad, it was a little humorous.