Yes. WiFi and Bluetooth connections are powered off during playback to conserve battery life during playback. If you're using Mighty with a Bluetooth accessory, then the Bluetooth connection is turned on but WiFi remains off.
Note: Mighty will not be discoverable by the mobile app during music playback. You must pause playback, then connect Mighty to the app. It takes a few seconds for Mighty to appear in the app after playback has been paused.