I don't think noise bothers them that much. Mine have never showed any difference in behavior during a storm nor are they afraid of the vacuum cleaner or other loud noises (8 year old boys having a playdate for instance ) ). I think she is fine ).
I didn't even think about how little the noise bothers her. She tries to play with the hose when I vacuum her cage. She also sits next to the TV when my boys are playing with the Playstation. I was just since I know my dog is hiding under the bed. He is a big chicken.
Mine don't pay any attention at all. They just snooze. Even with 45-50 mph winds, they don't stir. If you're worried she might be bothered, play a radio.
Dogs can hear much better than us and even chins, so it makes sense that they are more bothered by loud noises...chins have auditory properties very similar to us humans. Indiana University used chinchillas in research regarding auditory studies because their hearing is similar to ours.
I second the radio being left on. Our radio is on 24/7 and it calms the chins greatly. Other noises do not bother them near as much with the radio playing in the back ground. I have heard from some old old timers that without the background music on that no babies would be born 111 days after a bad storm. Its only hearsay and I have no proof so take it for what its worth.
I'm with everyone else, noise doesn't seem to bother them. What does bother them is large pressure changes. I have noticed health issues coinciding with major storms since moving to the south.