If it is the same cert it will see it as the same system. If the clone comes online you would get duplicate connection messages in your console saying there was a duplicate agent connection that is happening.
Well if you are trying to clear it out then you would do something similar to Include the LEM Agent in a Windows image - SolarWinds Worldwide, LLC. Help and Support which is very similar to an uninstall/reinstall
Definitely try it out to see what happens for you and if you are ok with it.