For example, I'm Hispanic-American. If I was such a badass at Gurkha training and beat all the best Gurkhas ever, will I be allowed to fight as one of them even though in not ethnically Gurkha?
By definition, Gurkhas are Nepalese soldiers; so I'm afraid not.
FWIW, how much of a badass you were doesn't really change anything anyway. They are not defined as an elite unite.
An exception, including my Grandfather, was that historically officers came from England and were seconded into the Gurkhas. I can't speak for when this practice ended.