The diet craze is nonsense and revolves around a significantly reduced caloric intake. I read that people consume only 500 calories per day on that diet... no shit you'll lose weight, you're starving yourself. The only benefit from adding HCG would be the potential for an increase in testosterone levels which may help muscle wasting in such a caloric deficit.
HCG replicates the body's signal to the testes to produce testosterone. This is valuable on a AAS cycle because exogenous testosterone (or any anabolic/androgenic) will shut down your body's natural test production: this happens because the body receives all this extra testosterone (from your injections) and decides that it doesn't need to produce its own anymore. The signal to the testes stops and then testicular atrophy occurs during the course of the cycle as they are no longer "in use". HCG will keep the signal going, keep the testes trying to produce, helping to avoid or at least limit testicular atrophy making the return to natural production post cycle easier.
That is, in simple theory, how it works. And it seems to have good carry over from theory to actual "real-life" application. .