On-device sensors in mobile systems, e.g., autonomous vehicles and AR/VR, use odometry for real-time positioning, but they risk capturing sensitive data of non-consenting bystanders. Prior works have investigated various privacy-preserving techniques to protect those sensitive data. However, it is still unclear about the impact of such approaches on the accuracy of odometry. In this work, we investigate the impact of various privacy-preserving obfuscation techniques on the accuracy of monocular visual odometry. We focus on three widely used obfuscation methods: Gaussian Blur, Gaussian Noise, and Laplacian Noise, applied to protect bystander privacy. Our investigation reveals that some obfuscation techniques can increase the odometry errors by up to 56.9%, while others surprisingly reduce the errors by up to 66.8%, compared to raw data. Our key findings indicate that data obfuscation primarily affects the duration of tracking loss in ORB-SLAM3, which is the main source of the errors, and successful relocalization immediately following tracking loss plays a crucial role in reducing the overall errors.