There are a few things going on. Increased T leads to increased E. The body increases SHBG in response to the E levels and the SHBG which then also reduces free testosterone.
When HRT is started T increases and free T increases, then E starts to increase and free T drops to a lower level. Somewhere in that change pattern, an interesting spike of libido occurs the greatly reduces after a while. Some of this is probably not just a response to the current T, FT, E levels, but to the transitions.
So if one could get blood work done at the right time, then tailor levels to stay that way, there might still be a loss of libido to some extent with those static values. Then there may be down regulation of receptors in the genitalia as well as the brain, creating or explaining the transient libido.
It is my understanding that increased E down regulates T by reducing LH and other hormones. And for those not taking exogenous T, when they reduced E production or reduce the effects of E on (some) receptors, LH is increased and T increases.
It is my understanding the the negative feedback is more sensitive to E than T. So there is some T feedback, but E is the dominant effect. It you were to block all estrogen, T would go up, but T itself would trigger feedback so the levels would not be unbounded or simply limited to the capacity of the testes to produce or the abolity to generate LH to stimulate them.
If one is not taking exogenous T and then takes HCG, I expect that feedback will simply reduce LH and test levels might not change at all unless one took enough HCG to swamp the system. At that point I would expect T levels to increase, but LH would be completely or mostly shut down. One would have to cycle to avoid damaging natural functions in the future.
For someone who needed HRT whose testes were functional and they had low test because of low LH, HCG could be used without exogenous T to increase T levels. But perhaps T would be needed in many cases to achieve the high normal ‘optimal’ levels that many progressive doctors seek.
Some folks simply respond with more E than others and some are harmed by this more than others. If we are talking about HRT, many do not get ‘abnormal’ estrogen levels. But the ratios of T:E may be more critical for libido in many cases. I wish I could find more info on that.
HCG for HRT simply saves the testes which then create some further increases in T that will be highly variable and individualistic. And HCG dosing has historically been all over the map. There is no link between HCG and E levels other than via the testosterone levels. The T levels can be managed to any arbitrary target, with or without HCG. So I see no need to couple HCG with E levels problems. Stated another way, you could get to the same T levels with or without HCG and the E situation would not change.
So these questions really need to be nailed down as to HRT or ‘recreational’, testes fully able or not, able to produce LH or not.
Note that if one takes exogenous T for a long time, the testes can atrophy and be permanently damaged. At that point, one is in the situation of non functioning testes, and HCG would not recover the testes or any natural testosterone production.
But if HCG is used along with T, the testes will remain functioning, producing testosterone and able to respond to HCG and if exogenous T is stopped, the testes are still working and one is then not sterile either.
That is not a clear answer to your questions, but perhaps what you need to know.