To combat privacy attacks that exploit the motion and orientation sensors embedded in mobile devices, a number of recent works have proposed noise injection schemes that degrade the quality of sensor data. Much as these schemes have been shown to thwart the attacks, the impact of noise injection on continuous authentication schemes proposed for mobile and wearable devices has never been studied. In this paper, we empirically tackle this question based on two widely studied continuous authentication applications (i.e., gait and handwriting authentication). Through a series of machine learning and statistical techniques, we show that the thresholds of noise needed to overcome the attacks would significantly degrade the performance of the continuous authentication applications. The paper argues against noise injection as a defense against attacks that exploit motion and orientation sensor data on mobile and wearable devices.