My Airpods are in my ears but the case is missing. It's possible it fell out of my pocket while walking around town. Is it possible to use the Find my iPhone feature to find just the Airpod Case?
Unfortunately, you can only find the AirPods themselves. The case itself does not support Find My iPhone. You can order a replacement case under the section “Replace a missing AirPod or case” on this page: https://support.apple.com/en-us/HT207581.
Yes, this should be possible as it is the case which uploads its position to the Apple servers - the AirPods which you actually stick into your ears can only play a sound. So if you select your AirPods in Find My iPhone, the location of the case will be displayed. If you have Find My iPhone activated for your iPhone, it will also be available for your AirPods. However, otherwise they will not show up in the app and you will not be able to track their location.
You can find more detailed information here: https://www.google.de/amp/www.iphonehacks.com/2019/03/how-find-lost-airpods-case.html/amp
Good luck finding your AirPods!