I've only missed about 6 home games in the past 18 seasons. I've only seen counting down the shot clock for the opponent work once, and that was before the new shot clocks which were visible from the side. In that case, the opponent player, off on the side, threw up a hurried shot as the band counted 1, even though there was about 3 seconds left on the shot clock and the right move would have been a pass to an open player.
Other than that, I've never seen it work. But most times, when the opponent has the ball and is focused on getting open or fighting for position, they hear the band start to count down the shot clock and realize that time is dwindling. They then look at the basket (or the opposite basket if their back is to the basket) and see how much time is really left. If the band hadn't counted the shot clock, time may have expired without them looking at the shot clock.
But even if you are right, and it works more than once every 18 years, even if it works twice a season, it still fails 4-8 times a season. So it hurts us far more often than it helps us.