Yes. That is the purpose of that function. The Watch will call 911 if you fall and do not respond on your Watch to tell it either you did not fall or you fell and are OK.
When I first received my Series 4 Watch the fall detection system seemed too sensitive. I received a few false notifications of falling. Each time I tapped on "I did Not Fall." I have not received a false notification in some time now. I know the Fall detection is working though, because I feel a few times while cross country skiing and my Watch detected it. In those instances I tapped on "I fell but I am OK."
If your Watch continues to be too sensitive about fall detection, an it has been updated to the latest version of the Watch OS make an appointment at an Apple Store to have a technician examine your Watch. Or contact Apple Support.