It would depend strongly on whether the phone is analyzing the data from the mic and reporting to a server "possible gunshot heard, GPS coords X,Y, volume-level 60%, gunshot-like-score 75%" or whether the phone is sending raw recordings from the mic to a server and trusting that the server is only checking them for gunshot sound (not, say, saving your private conversations).

And of course it's difficult for the average user of an app to tell the difference, or even for a tech savvy user to tell without investing some time and effort.