I stipulate that the following has nothing to do with the usual use of a skeg to balance wind, or for better control in following seas.
I have found that on calm water deploying the skeg on my Seda Ikkuma provides a small efficiency benefit.
Consider two boats with identical drag at a given speed, but one stiff tracking and the other loose. The stiff tracking boat will be more efficient at that speed because it will not 'waggle' side to side with each stroke. In other words, the waggle causes inefficiency. Plus, with the looser tracker one will be modifying the stroke a bit more for steering and/or leaning a bit more, both adding a bit to inefficiency.
So dropping the skeg on flat water adds a bit of drag, but makes the boat straighter tracking. The skeg on the Ikkuma is small and well shaped, so its drag is very small. The waggle of the Ikkuma is also small, but I sense that, with my stroke, I am a bit more efficient with the skeg deployed.
This will differ for particular boats and paddlers. Deploying the skeg on flat water in an already stiff tracking boat will add drag and not reduce the already small waggle very much. On a loose tracking boat, but using a high stroke with the blade very close to the hull, there may not be much waggle anyway. On a loose tracking boat like the Nordkapp LV, it may be more efficient to deploy the skeg on flat water. Especially with a longish paddle and a low stroke.