No. Pairing is only done between the handlebar unit and thru-axle. If you swap a Classified hub with another Classified hub, the pairing is not impaired. In other words: after a wheel-change you can set off immediately.
Yes, you can use through ANT+ to display the Classified hub gear-status on any/most ANT+ computers. For pairing, refer to the instructions of the ANT+ computer.