A skimmer can definitely be "too big" for a system.
One aspect is the physical ability to skim. That is, the diameter of the neck & bubbling power of the pump are so large that it would take a very large amount of DOCs to fractionate any amount of foam. In a small tank that is lightly stocked, the required level of DOCs to foam would be harmful to most sensitive coral. Dont confuse not foaming with the lack of DOCs beacuse if you feed, theyre definitely in there. In this case a smaller skimmer would be able to foam when a larger one couldnt. An undersized skimmer would foam even earlier but couldnt keep up, that is, it couldnt remove organics as fast as you help make them. Size does matter, and not just bigger is better.
Another aspect is the goal of skimming. How low do you want the DOCs to go? Obviously with SPS the less the better. LPS, im not sure, but probably a little bit more DOCs is ok. Zoos & softies may not want it as low. As for non-photosynthetics, a skimmer directly and indirectly competes with the coral for food, so skimming would not be good. The best NPS tanks ive seen are dirty, "overfed", not skimmed, but get water changes frequently.
HTH