Pickup of more distant sources from at or beyond the room's critical distance of reverberance entails quite a different acoustic situation though, and I suspect it might not work as well there, at least in comparison to just going to a more directional pickup pattern.
Conceptually, it should be able to reduce the level of direct arriving sound from the rear and sides, but only above some threshold frequency determined by the diameter of the sphere. Frequencies lower than that have wavelengths long enough that the spherical baffle will not be effective in blocking/reducing them. In other words, regardless of the microphone pattern used, the isolation the hemispherical shell provides will be frequency dependent, with increased isolation at higher frequencies and none at significantly low frequencies.
Consider an omni placed in it. The resulting polar pattern will remain omnidirectional at low frequencies, but will be directional at high frequenceis, as determined by the geometry of the mic within the hemispherical window 'opening' through which direct sound arrives.. along with some acoustic diffraction around the lip of the opening at some frequencies. It will have a complicated polar with regards to pickup of sources not directly in front of the window.
Seems like it would be useful when one wanted to use an omni for whatever reason, such as its flat natural response without proximity effect, yet some degree of increased ambient isolation is needed. Like for on stage percussion table stuff and the like, similar to how the KC guy last summer seemed to be using one.
Not saying it couldn't work for taper situations.. thinking specifically of how I've used the cushioned backs of front row seating as a rear baffle to reduce pickup of audience sound into omnis placed low up front in the past. That baffling should also produce a frequency dependent reduction as mentioned, and in practice it worked pretty well in reducing level and presence of the audience reaction into the omnis.