It's difficult to see much benefit to this. Counter-rotating props make sense because the second prop minimizes residual swirl (which is basically wasted energy) - at the price of massive noise from the second prop cutting through the vortices of the lead prop. With a ducted fan you remove the swirl with exit guide vanes so there is little wasted energy (at the price of increased weight and drag from the duct).
With a ducted counter-rotating fan you don't need the exit guide vanes, but you still need that big, heavy duct, and you're still making massive noise - yes the duct helps limit the noise, but it'll still be noisier than a simple fan. But the real down side is now you effectively have a two stage fan which means a much higher pressure ratio through the fan. A single stage fan (or compressor stage) is good for about a 1.5-1.6 pressure ratio. Double that and you're over 2, and anything over 1.9 means supersonic exhaust at takeoff. Very bad news for exhaust noise (we're basically talking a JT-8D fan pressure rise and resultant level of exhaust noise).
A two stage fan also contrary to maximizing efficiency - propulsion theory says max efficiency comes when you accelerate an infinite amount of air an infinitesimal amount - that's the fundamental reason why big turbofans are more efficient that pure jets and the reason why we keep moving to ever higher fan bypass ratios.
This looks like a whole lot of complexity with little or no benefit. The only way I can see this making any sense at all is for something designed to go supersonic (where you'd want a high fan pressure rise).