If the ducted propeller really increases efficiency, we would see more of these

[![Fanliner][1]][1]

Rhein Flugzeugbau Fanliner (picture [source][2])

and fewer of these:

[![Socata TB-9][3]][3]

Socata TB-9 (picture [source][4])

The ducting has benefits when

 - the [disk loading][5] is very high. This means the propeller diameter is small for a reason. Since efficiency tanks with decreasing propeller size, another consideration forces the propeller to be small. This would be the [tip Mach number][6].
 - the propeller noise [would be unbearable][7] without the fairing. Again, this is the realm of highly loaded propellers with high tip Mach numbers.
 - the flow passing through the propeller needs to be conditioned such that regardless of flight speed the [flow speed at the disk is almost constant][8].

In short, this benefits turbofans which fly at transsonic speed.

For slower vehicles with less power hungry propulsion systems, [the disadvantages will prevail][9]:

 - Friction losses on both surfaces of the fairing easily eat up any gain from reduced tip losses.
 - The weight of the fairing creates induced drag.
 - Also, the fairing costs more to build and maintain than leaving it off and using a larger, more efficient propeller.

> Could ducted propellers improve efficiency in small drones?

Clearly no!

  [1]: https://i.sstatic.net/eb3DB.jpg
  [2]: https://www.aerokurier.de/motorflug/rfb-fanliner-1978-flugbericht-rhein-flugzeugbau-fanliner/
  [3]: https://i.sstatic.net/KG80G.jpg
  [4]: https://flyteam.jp/photo/2273686
  [5]: https://aviation.stackexchange.com/questions/27300/how-does-a-fan-differ-from-a-propeller/27303#27303
  [6]: https://aviation.stackexchange.com/questions/13837/given-the-same-engine-why-install-a-gearbox-on-a-turboprop-but-not-on-a-turbofa/13839#13839
  [7]: https://aviation.stackexchange.com/questions/87658/is-there-an-example-of-a-classic-aviation-engineering-moment-when-engineers-had/87684#87684
  [8]: https://aviation.stackexchange.com/questions/62608/can-the-maximum-thrust-of-a-turbofan-engine-be-estimated-by-its-intake-diameter/62617#62617
  [9]: https://aviation.stackexchange.com/questions/9940/what-are-the-advantages-and-disadvantages-of-ducted-fans-in-designs-such-as-the/9949#9949