The reason people get away without feeding their corals in larger tanks is due to feeding the fish. In a pico, there isn't sufficient wate and missed food to trickle down to the corals (depending on what your definition of pico is. For me, there are only a couple species suitable for the largest of picos and even at that, there isn't much bioload). There are tons of research articles that discuss how the transfer of nutrients to the coral from xoozanthellae is insufficient and does not provide everything necessary for healthy growth, or anything beyond stasis for short periods.
From my research, I believe that you can't have corals without feeding. People that claim to get away without feeding are in fact indirectly feeding their coral by feeding their other inhabitants. I noticed recently that a bunch of people were blown away by the growth and color that an individual was getting in their frag tank, but they couldn't seem to grasp the fact that the difference was that the high growth tank was getting fed while they were adamantly refusing to feed in an attempt to keep the lowest nutrient levels possible.
In a pico, things will slowly starve out without feeding. Picos can easily be overcome with high nutrient levels, but at the same time, extremly large water changes are easily (and inexpensively) accomplished and simplify the process of keeping nutrients in check while keeping parameters in a narrow band. My pico was doing quite well with very heavy feedings every day or two with bi-weekly or weekly 100% water changes. Things went down hill when I got busy (100+ hours of school work a week) and wasn't able to feed and perform water changes as regularly. Parameters were low and stable, but growth stopped and started going in the opposite direction after a couple of weeks.
I don't think you can keep a successful pico without feeding.
