Your birdsnest is probably growing fast for reasons other than the accidental damage. It's most likely in a growth phase because it's getting everything it needs to grow.
Corals aren't like some garden plants which definitely respond to pruning with accelerated growth, to the best of my knowledge. However, larger colonies can begin to shade themselves so breaking off a branch will give several smaller branches below more light and they will grow out as a result.
Personally I wouldn't prune for growth. Just keep doing what you're doing. But if you want frags to trade, sell or mount elsewhere, or the coral is violating another coral's territory....I say frag away! Just my 2 cents there.