In general, anything that reduces the magnitude of tip vortices will increase efficiency, so producing more output power for a given input power. A simple ring around the tips of the prop will do this to some extent.
Adding a convergent duct around the prop (like the Kort and Rice nozzles) tends to increase the velocity ratio across the prop disc and duct combination, so increasing the mass flow rate and generating more thrust for a given diameter (with a commensurate increase in the power absorbed by the prop). In effect, a prop in a convergent duct behaves somewhat like a larger diameter open prop.
The tradeoff comes when comparing the efficiency improvement that comes from the reduction in vortex magnitude with the power needed to overcome the additional drag created by the duct. As has already been mentioned, the break-even point tends to be just a few kts; a ducted prop is unlikely to be more efficient than a properly sized and pitched open prop above about 10 to 15kts or so.