You can't get Ramsay Hunt syndrome (RHS) from someone who has it, but the blisters have the live varicella zoster virus in them. So newborns and people who haven't had chickenpox or been vaccinated against it can get chickenpox from someone with RHS.
People who have had chickenpox or the chickenpox vaccine can't get herpes zoster oticus from being around someone with RHS because their immune systems have learned how to fight the virus. They also won't develop chickenpox again for the same reason.