"Fake it till you make it" doesn't mean pretend to be happy until you are happy. I committed to a relationship I wasn't happy in, a career I wasn't happy in, and hobbies I wasn't happy doing, all because I wanted the approval of others. A divorce, career change, and hobby swap made me much happier.
Yeah, fake it till you make it only applies to overcoming self doubt, and should not be used to dismiss glaring problems. It certaibly doesn't work as a cure all for actual problems.
It can in rare cases work for happiness, but only if the reason is one that is just based on self doubt while things are actually going well.