There is no proven science as to whether dosing it will be helpful but it suggests dosing it may be beneficial It seems like an excellent way to add some nitrogen and organic C.
Whether or not you choose to put l aspartic acid in your aqaurium is none of my business or concern.
However, misinformation about the nature of aspartame and aspartate and misrepresentation of what a cited study actually says needs to be addressed.
In brief corals use aspartate and need it, but they may have limited ability or no ability to synthesize it and may take it up from the water of food sources.
The study you cited further supports this hypothesis . It doesn't discount the role of aspartic acid at all since it is identified as one of the 17 amminos present in corals . It does, however , note that the researchers were unable to trace synthesis within the coral. That suggests to me that the coral may be getting it at least some of it from the water or perhaps food sources and further that dosing it is likely a good thing beyond just a good way to add nitrogen and organic C.
In the abstract of the study they clearly state:
Animals rely on their diet for amino acids that they are incapable either of synthesizing or of synthesizing in sufficient quantities to meet metabolic needs. These are the so-called 'essential amino acids'. This set of amino acids is similar among the vertebrates and many of the invertebrates. Previously, no information was available for amino acid synthesis by the most primitive invertebrates, the Cnidaria. The purpose of this study was to examine amino acid synthesis by representative cnidarians within the Order Scleractinia. Three species of zooxanthellate reef coral, Montastraea faveolata, Acropora cervicornis and Porites divaricata, and two species of non-zooxanthellate coral, Tubastrea coccinea and Astrangia poculata, were incubated with <sup>14</sup>C-labelled glucose or with the <sup>14</sup>C-labelled amino acids glutamic acid, lysine or valine. Radiolabel tracer was followed into protein amino acids. A total of 17 amino acids, including hydroxyproline, were distinguishable by the techniques used. Of these, only threonine was not found radiolabelled in any of the samples. We could not detect tryptophan or cysteine, nor distinguish between the amino acid pairs glutamic acid and glutamine, or aspartic acid and asparagine. Eight amino acids normally considered essential for animals were made by the five corals tested, although some of them were made only in small quantities. These eight amino acids are valine, isoleucine, leucine, tyrosine, phenylalanine histidine, methionine and lysine. The ability of cnidarians to synthesize these amino acids could beyet another indicator of a separate evolutionary history of the cnidarians from the rest of the Metazoa.
So, they couldn't distinguish pairings involving aspartic acid;that in no way says it wasn't there but quite the opposite. They were also only able to detect 8 that were made by the coral and aspartic acid is conspicuosly absent from that list of 8.
Even though later in the study Asx ( choice between aspartic acid and asparagine) is listed in table 1 as an essential amminio acid for cnidarians.