It certainly can work, see a fantastic example
here.
I've always wanted to try this out with those little emax motors they use on the gremlins.
The thing about using a ducted prop is that the prop is normally a lot larger radially than an equivalent EDF and produces much less thrust:
a 3" 3-bladed prop on an 1106 will produce 250g on 3s, whereas an equivalent sized fan (~70mm) produces upwards of 800g of thrust at the same voltage.
To get the same thrust out of an equivalently sized prop, you'd have to spin it really, really fast, which sort of negates the purpose.
That being said, the prop would be vastly more efficient: The 3" prop above draws around 90 watts whereas the EDF draws about 500.
Another advantage of the prop is that the power system weighs much less, but that means that the structure of the plane itself now constitutes a much more significant portion of the weight. If you're planning on using a ducted prop, you'll have to build really, really light, simply due to a massive reduction in thrust over an equivalent-sized EDF.