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 uses the sensor.



From Techradar:

Always-on Kinect not so scary anymore? Microsoft has previously stated that the Xbox One Kinect would be required for the console to function, but it now sounds as if it's limited to Kinect-enabled situations, just as it is on Xbox 360. That's good news for privacy advocates who feared that an always-on Kinect would become a highly advanced, 1080p spying gadget. Microsoft, after all, has allegedly worked with or was forced to help the FBI spy on its customers. So many 180s, Microsoft is spinning out of controlThis is the latest retreat for Microsoft in a series of strategic missteps.Xbox One was thought to be hostile to independent game developers by requiring a publisher, leading Sony to take advantage of the thriving garage-based software community when touting PS4.

  Microsoft: Xbox One won't require Kinect to function