Don't think of aminos as supplementing the actual aminos used in the organic process. First, nobody has any idea if any coral or organism are deficient in any, but it is not likely since they do OK in nature. Second, nearly no products say what are in their supplements, so you have no idea what you are adding... and those that do only have a few kinds and not all. To do any good to the protein process, you would need several kinds which would differ for each coral/organism. The only hope that aminos do anything is that a coral synthesizes them whole, through the slime coat, and gets the nourishment - this likely happens, but there is no idea at what rate. Single cell organism, bacteria, algae, etc. all will use them too. Your corals will get some, but they lose out on a surface area math problem in a real tank... which is why they can do better
I won a big bottle at a local raffle. Used all of it and could not tell a difference. Could not tell a difference when I stopped. For me, amino supplementation is just the fad of the current times. Many fads have come and gone with all kinds of "science" and sworn testimonials from reefer-users only to be a punchline now. Coral Snow, Phytoplankton, Oyster Eggs, Essential Elements, etc. My guess is that Aminos will soon be a punchline too when the next thing comes about... maybe Kryptonite, Adamantiam or Vibranium.
The bottom line for me is that they don't likely hurt unless you are feeding something that you already hate like a dino bloom, hair algae, etc. However, they are certainly not necessary. ...so use them if you want.
Anybody considering dosing aminos can also look into dosing ammonium which likely will very much do the same thing and is cheaper. Of course, you can just keep the fish fat and happy too.
Perhaps the most important thing to learn and remember is that Nitrate is probably not doing what you think that it is if you dose it. Host have to convert it back to some other form for the microalgae to use it... and not all can do it. The host can convert it, it is costly. In the end, you are not likely getting any or much nitrogen to your corals by dosing nitrate, yet lots of people think that they are feeding them. Be smarter than most of them. The largest consumers of nitrate directly are anoxic bacteria and macro algae, that I know of.