I did a lot of research on this a while back. First, aminos are not likely in short supply for your corals anyway. Second, nearly nobody lists which ones are in the product (there was one that did at the time) so you don't know what kind of impact that they can have. Third, you likely need all/most of them to do any real good in the way that an amino is supposed to act as a branch chain building blocks and just one or two of them won't do this since you don't have their friends along for the party. Not all kinds would ever likely be stable enough to get dosed in a bottle. A pHd that helped me with some of this compared the bottled amino supplements to a human one that might label as healthy fats and you don't know if trans or omegas are in there... HUGE differences.
The best that they do is to maybe get broken down by some organism, or the coral absorbs them through their slime coat and some nitrogen consumed but it is not used as a true BCAA. It is more likely that they don't really do anything that you cannot get from some more fish food or maybe adding some ammonia. They also likely do not hurt anything unless you already have too high of residual N and P, so if you feel that they help, then go for it. In the end, what goes it still has to come out in some form.
If you do believe that the corals can absorb the aminos raw and get energy from them, then they also have to win a math game. Nearly anything else on a surface in your tank can absorb them too. ...so with corals, and especially frags, having such small surface area, they are not going to get much of what you dose. Colonies can get more, of course.
There is no chance that any hobby based company could afford, nor did spend, enough money to actually see what difference aminos actually make. They are just probably guessing... so not on Vibrant level of just flat-out lies, but also probably not going to do what they say that they do on the bottle. I might be more inclined to try some in a frag system where introducing even an unknown might be good to get some stuff into the system, but in a full-blown reef, I just don't see how they help much over what is already in there.