No its not actually part of the steering wheel.
That clip and the wire attached to it are part of a capsule that sits behind the wheel and allows the electrical connection to the airbag even when the wheel is turned.
Because the airbag is a safety critical component, they cant use a slip ring arrangement like they do for horns.
The capsule has a coil of wire inside thus its name "clock-spring"
From the picture you have shown the connector as being slightly damaged but its not clear if it will go back into the socket or not, have you tried ?
For safety, you should disconnect the negative terminal of the battery and wait 20 mins before re-connecting it or you could be sucking on a zeppelin.