According to The Guardian, GCHQ is already monitoring and recording webcam images of more than 1.8 million Yahoo chat users under the "Optic Nerve" surveillance program. The agency was evaluating the possibility of expanding the program to include Kinect. Snowden's leaked documents didn't include the final decision, but they suggested that Kinect produces "fairly normal webcam traffic."
Responding to The Guardian report, a Microsoft representative said that "Microsoft has never heard of this program. However, we're concerned about any reports of governments surreptitiously collecting private customer data. That's why in December we initiated a broad effort to expand encryption across our services and are advocating for legal reforms."
Xbox One was originally designed not to work if Kinect isn't turned on but Microsoft reversed that decision before launch due to fans out lash and privacy concerns.