I don't think this will cause the machine to have a new PCID which is what will cause you to need to enter a new license.
Most users have self managed licenses and would be able to go to MachSupport.com and log in to create the new license. If you already had the maximum number of concurrent licenses, you would need to remove one of the old ones first.
If you do not have a self managed license, consult with the company that issued your license.