Yes, few fish and 20% water change a month. My understanding is the main benefit for skimming is to remove DOC to keep them out of the nitrogen cycle thereby keeping down the Accumulation of nitrate. I've run this tank for two years with zero nitrate. I also broadcast feed twice a day reef roids live and frozen food.
with few fish & 20% water changes DOC/TOC is unlikely to be a problem.
Yes, skimmers remove some DOC before it mineralises, but is high DOC/TOC a problem despite reasonable nitrogen & phosphate levels?
From Feldman
https://www.advancedaquarist.com/2011/3/aafeature
Not surprisingly, the tanks with "unpurified" water exhibited TOC levels greater than those seen with the skimmed/GAC-filtered tanks. The "purified" aquaria's TOC levels fall within the typical TOC range seen on authentic, healthy reefs (Feldman, 2008); the passively husbandry tanks were 2-3x higher.
The observation that, at least among this small set of aquaria examined, the water within the skimmed/filtered tanks had only ~ 1/10th of the population of bacteria that the unskimmed/unfiltered tanks had was a real surprise. It speaks to one aspect of aquarium husbandry in which a perhaps important parameter (?), water column bacteria counts from authentic and healthy reefs, is not reproduced at all effectively in these home aquaria.
Sensitive corals, like Acropora, do not thrive in the high-bacteria-count/high-TOC-level tanks examined, although soft corals do well (see pictures). On the other hand, SPS corals do well in the low-bacteria-count/low-TOC-level tanks (Fig. 6). These observations raise a number of questions, chief among them perhaps are, (1) "Do water column bacteria counts have any relevance to the short-term or long-term prospects for maintaining SPS in captive aquaria?", and (2) "What is the relationship between TOC and water column bacteria population?"