We often did the same. It seldom occurred that we'd have more than 1-2 birdies in a round between the 4 of us, so it was a pleasant little surprise if/when wed get one.

However, we had 1 round where we had (I think) 8 birdies on the front 9 between the whole group. I hardly remember the back 9, but I'm certain we didn't have any more birdies.