No offense to 單身老貓 but I believe vaccine does not apply here since the gentleman is a carrier and vaccine is not a cure. It is non-cureable.
By the book he will never get GC but if he can prove that it is not a danger to public health, then it is pos*****ile.
But it is for sure that he lied on his visa application about "Have you ever been afflicted with a communicable disease of public health significance or a dangerous physical or mental disorder, or ever been a drug abuser or addict?"