This is quite a "controversial" topic and it is not well understood yet.
We know that corals
can biosynthesize most amino acids on their own or together with the zooxanthellae and/or gut bacteria, but we don't know if they additionally rely on getting these amino acids from the water column. However, we know that they consume many amino acids fast when they are available, but it is possible they just use them as a nitrogen and carbon source which ammonia/nitrite/nitrate and carbon dosing would achieve as well.
In reef tanks most amino acid concentrations
seem to be far lower than in actual coral reefs, which the community was able to find out using Organo-MS analysis results. Amino acids also have a
very short half-life in reef tanks, and you would need to dose them very frequently to keep levels "stable".
I'm currently trying to
gather ideas for experiments, which hopefully will shine some light on the actual benefits or disadvantages of amino acid dosing.