No, if you have been handling your chicks, they won’t die from fear of the dog, but can get scared and injure themselves.
As with anything do it in stages. Arrange the brooder so they can see OUT and have your dog away from the brooder so they can see them before the dog is in their face. Do a couple distant interactions before doing anything closer. Keep them separate until the dog no longer has “aggressive” curiosity.
I would also suggest introducing them BEFORE the chicks can fly. Something darting past their face will activate all their instinct to retrieve.