The dogs will only upset the chickens if they charge the run fence, snarling and acting like they want to eat the chickens. While it's possible for a chicken to die from fear and shock, it's more likely the stress will take its toll in poor egg laying, conflicts among the flock, and compromised immune systems due to chronic stress.
However, if the dogs are kept away from the run and not permitted to behave in a predatory manner, and all they do is bark, the chicken will learn to tune out the noise.
In short, noise is not a problem for chickens. Predators and predatory behavior is a huge problem, and dogs are predators whether or not they lick you and love you to bits.