I'm not a doctor, but I believe they will fight against each other.
Clomiphene should help to speed up the HPTA adjustment, helping to increase LH and FSH signals to the testes.
But HCG inhibits also LH signal so I guess it is too much medication for nothing.
There's seem to be a misunderstanding regarding "suppression" and "inhibition" of LH and the supposedly cancellation of benefits of
enclomiphene or clomid and HCG.
hCG (human Chorionic Gonadotrophin) does not "suppress" the pituitary or "inhibits" LH production. hCG mimics LH which causes the testicles to produce more testosterone, as a result, the level of estradiol in the blood increases due to a process known as aromatization. As a result, this level of estradiol send a negative feedback signal to the Hypothalamus and the Pituitary which interpret this increase of estradiol as "there's too much testosterone, we need to back down" and that's how LH decreases, in a failed attempt to regulate the amount of estradiol in the blood. If the levels of testosterone are too high, then the level of estradiol are also higher, which could eventually result in the Pituitary completely stopping production of LH. If this situation persists for a very long time, eventually the pituitary could be "suppressed" (atrophied) . As you can see, it's a dynamic process, not that hCG goes and obliterates the pituitary, or takes it hostage so it cannot produce LH
Based on the above, and understanding that the Pituitary produces LH in inverse proportion to the levels of estradiol, wouldn't it be possible to fool the pituitary by making it blind to that increase in estradiol, so it continues to produce LH?
Enter
Enclomiphene (or Clomid) which is a Selective Estrogen Receptor Modulator (SERM). What it does is that (and this is a very metaphorical and simplistic way to describe it) it plugs the estrogen receptors in the hypothalamus and pituitary so they become "blind" and think "hey, there's no estradiol, so we ned to produce more LH to increase testosterone production"
That's why hCG and Clomid don't "fight" each other, on the contrary, they could be synergistic, particularly for fertility reasons and they are frequently used together for that purpose.
hCG will cause direct testosterone production (assuming the Leydig cells are in good condition, that is, no primary hypogonadism) and increase intra testicular testosterone which is required to produce sperm. Clomid, will also keep production of LH from the pituitary, but more importantly, ramp up FSH production which is necessary for sperm as well.
Hope this helps dispelling the whole "hcg is suppressive and fights clomid" myth. As an anecdote simply, I along many others, have been on an doctor supervised
enclomiphene + hCG protocol and can attest to the results.
I know many would ask if the same principle applies to TRT + Clomid. In principle it should, yet it seems that there's also androgenic feedback on the hypothalamus/pituitary that is too strong for the SERM to overcome, or some other mechanism that at least I am not aware of, but many have tried it without success. I do not have practical experience, but it could be, just maybe, that perhaps if you inject less than 5mg of testosterone per day, Clomid/
Enclomiphene could still do something to keep the HPGA working. Just a hypothesis.
On the other hand, it's well recognized that hCG while on TRT would help prevent the Leydig cells from atrophy and could in some cases, help preserve fertility, depending on dose and protocol, and genetics.