There seem to be two questions here:
1) Can the mobile app be stopped while the hardware keeps running? Yes it can. You can exit and kill the app just like any other app and the hardware keeps running. It keeps on taking images, guiding, etc.
2) How to stop the hardware. Open the app on your mobile device and go to the WIFI settings. There is a red icon in the upper right that allows for clean shutdown of the hardware.
With hardware I mean the ASIAir device that the cameras and mount get connected to.