Shrouded props do work and the increase in static thrust can be significant. The critical aspect of the configuration is that it must be designed for the condition you anticipate in its operations. As such, for a vertical lift platform or similar, the design must be optimized for a static condition or at least, for very low speeds.
The additional performance comes from three areas of design: One, the higher efficiency the prop can operate under with the tip seal the shroud provides; two, the suction gained off the leading edge and three, the surface of the expansion nozzle aft of the prop disk.
I've been involved in a couple of shrouded prop developments - on the first one (hydrofoil with two C-130 shrouded props), we showed that forty to sixty precent of the operational thrust came from the shroud. The second was a new shroud/prop design for the military LACV vehicles (hovercraft) - there we were able to show over 100% more thrust over the standard vehicle's propulsion with a prop/shroud that was about 70% of the original prop's diameter.
And currently I'm working on a six to eight place amphib that will also use a shrouded prop and here too we're seeing an increase in thrust of over 40% for the take-off and climb conditions.