I'm positive my fish don't get all the food I feed.
I'm positive the corals don't get all those leftovers - but accidents happen
I also have been happiest with the tank's overall health when feeding a DIY fish food - which has been blended in part, and has some small particulate + small meaty foods involved [CE, a couple varieties of powder/particulate food in small amounts, rotifers, and smaller pieces of a variety of seafood/shellfish].
Not really heavily feeding towards the corals - but the food itself has some that is likely too small for the fish to bother with.
As for how it gets to coral, how much it helps, whether it needs special attention - IMO that's quite a question. Food's path to the coral could be simple - or quite convoluted.
Were the fish eating and pooping it?
Were the corals catching some?
Was the bacteria/etc eating it and then getting caught by the corals?
Were the microfauna booming and feeding things?
Was the bacteria on the surface of the coral getting it and then providing it to the coral?
Were there any of the many other ways moving the stuff that I turkeybaste to the coral?
Heck if I know, but all seem possible.
I always aim to feed just barely under what I can export - and to export a lot. I figure that if I want it to grow fast, color up nice - that I'd like to give it all the energy it could possibly use; provided I'm not fouling the water in the process.