The coaches are going to know how many fouls each team has whether it's on the scoreboard or not.
That said, the timer is an official under your control. I wouldn't recommend it, but you could have them not put up team fouls. It's helpful for the fans (and the refs) to have, though.
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"To win the game is great. To play the game is greater. But to love the game is the greatest of all."
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