I can attest, when the woods assume natural sounds of 'chatter' and being, squirrels are active. If a person, or bird, or another animal, or whatever, alerted, they will become alerted as well. During this time they'll hunker down, sometimes in place by flattening themselves on the limb they stand, for 20-30 min until 'normal' activity resumes. That's why sometimes, if a hunter suspects being detected, they take two quarters with the ridges on the outside, and rub them together. This is a good imitation of the sound of squirrels cutting (eating) various nuts. It relaxes the squirrels and encourages them to resume normal behavior. Same with some aggressive rustling of leaves, imitates the sound of a squirrel burying or foraging.
TL;DR Natural sounds are relaxing, but they also know when other species become alerted to a threat and act accordingly.