Yah. But for a very specific purpose: short-term boost to allow better NA engine speed change under load.
As a supercharger, this idea suffers from the same problem as electrically-driven superchargers in general -- very high currents are required for the desired hp. of boost. The efficiency of a ducted fan generally suffers when the airflow through the duct is not smooth, and I might add also suffers when back pressure is high enough to spoil the flow. I would certainly think that an enclosed centrifugal design would give you better effectiveness than a df if the engine requires boost at widely different rpm ranges.
A generally preferred idea is the use of the 'electricity' to run a motor in the center section of a turbocharger, to spool the compressor up more quickly on engine speed change. This is a popular design idea on large diesel engines, and people have tried to promote it as a 'better' turbocharger for performance applications. Here the motor only serves to provide sufficient boost to spin the engine up to the point that the exhaust-gas flow induces adequate turbo boost registered at the intake valves (e.g., net of all pressurization and lags in the intake tract, intercooler, etc.) You are NOT trying to run the turbo as an electric supercharger. (I have also researched variants of this approach that use pressurized gas on either the turbine or the compressor vanes -- the latter either being an oxidizer or a combustible gas that supplements the principal engine fuel.)
On a carburetor, you have the additional problem that increased boost pressure blows the fuel out of the jets. That usually requires some form of external enclosure -- you've seen the polished aluminum 'pot' on the E-bird motors, right? In addition, I would expect the relatively primitive mixture adjusting capability of most carburetors to provide lousy emissions numbers over the desirable range of boosts. My advice to potential supercharger developers is to go directly to port injection or modulated DI, with the fuel admission programming using some form of pressure sensing to determine the boost and flow. This used to be expensive ;-}
but is now pretty cheap and do-able.
I would expect that a ducted fan would only be useful for sustained power output, in situations where the relatively steady-state flow in the intake tract matched the flow characteristics through the fan and duct. Variable vaning on the fan would provide a wider potential range, but probably isn't worth the cost for the linkage, actuators, etc. Likewise, 'feathers' or other variable geometry on the tail end of the duct might provide some measure of optimization. You begin to run into other problems, though: the physical size and packaging considerations -- presuming you want to run this thing in a car. Not to mention the incredible fun you are going to have with air filtration...
I do truly wish that electric supercharging worked -- I'd start in working out how to put some of the things on my M73 BMW motor as quick as I could figure out how to reverse-engineer the engine control chip... Unfortunately, even with the wonders of NIB magnets, the energy density and resistance-heating problems limit the developed HP to well below what any halfway-competent shaft-driven SC is expected to need.
I encourage you to look at some other lists to read discussions on the technologies involved...
RME