Are there any propeller or fan designs that hold the propeller or fan in the duct and do not have a boss or propeller shaft? This could reduce the drag of the centre. Are there any other advantages?
Perhaps an aeronautic version of one of the Voith maritime systems? This one appears to be electrically powered. http://www.voith.com/en/products-services/power-transmission/voith-inline-thruster-voith-inline-propeller-11014.html (watch the "installation" video). Also, this video explains the concept a bit (for maritime applications)
I suppose if you could arrange a lightweight frictionless magnetic ring bearing (possibly integrating electric drive), and/or peripheral drive linking system, it might be worth it if you needed to have two or three smaller fans beside each other, driven by a single core, rather than a singe large fan, in order to reduce fan/nacelle height. (imagine a B52 nacelle with one side shortened to just a fan cowling) I doubt that this would reduce overall drag, though, but I am intrigued by the concept of the greatest chord of the blades travelling the fastest.
You're thinking of an exoskeletal engine. They've been studied, and have lots of theoretical advantages, but the major sticking point that's kept them from being used so far is that we don't currently know how to make bearings suitable for supporting the large spinning rotor drum.