When someone has a serious mental illness, playing along with their illness is exactly the wrong thing to do.
Some people live their entire life with long term mental illnesses. This is no different from people who suffer from Body Integrity Identity disorder. There are people out there who literally feel as if they should have an arm or a leg amputated. Some get over it, some do not, but the mental problem of someone who thinks they are the wrong sex is no different from someone who thinks they should have an arm or leg missing.
That some form of treatment doesn't work does not mean someone is mentally healthy. It just means they haven't figured out or can't treat the cause yet.