Yes, you can unplug the Kinect sensor without your Xbox One turning into a useless brick. In an update to an ask-me-anything style Q and A hosted by IGN, Xbox One Chief Platform Architect Marc Whitten was asked if the console would still work if the previously mandatory Kinect sensor were to fall onto a hardwood floor and break. Whitten responded that "like online, the console will still function if Kinect isn't plugged in, although you won't be able to use any feature or experience that explicitly used the sensor."
Whitten also detailed that you can turn the sensor completely off in the One's system settings. "When in this mode, the sensor is not collecting any information," Whitten said, adding that it's still in use for IR blasting in this configuration. He added that "entering into a required Kinect experience" with the sensor off will prompt you to enable it before proceeding. Like earlier announcements concerning daily DRM check-ins, indie self-publishing and headset inclusion, Microsoft is backpedaling on unpopular news from the Xbox One's launch.