The short answer is, it depends. When Propeller is running in the background on your smartphone or tablet, it's occasionally checking to see if the sensor is trying to send data. This action should have a very limited impact on the battery life of your device. Your battery usage also depends on how frequently you're opening the app to check your data and add additional information, just like with any other app.
If you're concerned, check the battery usage information on your smartphone or tablet. If you're unsure how to do this, contact your mobile provider or smartphone help desk.