While they are highly autotrophic even sps need some carbon based foods as well as nitrogen for protein ,dna etc and phosphorous. Surface reef waters are low in nitrogen and phosphorous, .2 to .5ppmm NO3 and.005ppm PO4.Corals from deeper waters are used to levels 5 to 10xhigher. But even the surface levels are constant and not 0.
I have not feed any small micron coral foods in months . Tried Coral Frenzy which has small micron foods in it for a while but didn't notice any changes.
However, I have over 40 fish in the 550 gallon system which are brodcast fed a mix of mysis, brine, mosquito larvae(blood worms) and cyclopeeze, which may be small enough for many of he sps, 2x per day. No socks or other mechanical filtration are used accept occasionally during maintenance or rare lanthanum chloride dosing.. Several refugia for cyptic critters and pods also contribute to the food chain; I hope. Dosing vodka and vinegar daily povides bacteria and acetate which may also help..
I may try some aspartic acid from I herb.com,an amino not syntesized by corals but one which they use.
Overall, keeping PO4 and NO3 low(FWIW, system levels are PO4 .04ppm, NO3 .2/.5ppm) trumps heavy feedings or amino supplements and I'd watch those levels closely when new feeding routines are applied.But it is possible to create anorexic corals but it is unlikely in a reef tank with fed fish, in my opinion.