Guess I will weigh in here. There are fairings then there are aerodynamic fairings. Anything that reduces drag is a benefit of course, but unless one has access to advanced programs, a wind tunnel or both a design can be a crap shoot. Looks slick doesn't necessarily=slick. The holy grail of aerodynamic shape is one that separates the air, keeps it attached to the shape and puts the flow back together with no turbulence, a tall if not impossible order. A Cd of zero
All that said I think a faired bike is an interesting idea. A recumbent would be the best choice to reduce the size of an upright bikes cross wind flat plate, though I think maybe a more efficient fairing could be built for the upright. The flowing air has to be accounted for over the bottom as well as sides and top. The bottom is where most fairings lack. A trike off the get go is going to be harder to achieve a low Cd with just by the shape.
In the real world a practical vehicle probably isn't gonna get real close on the low Cd arena, but surely the benefits of a decently designed shell will increase efficiency of either pedal or motor drive as well as add weather protection.
Being a avid aircraft restorer I would favor a fabric design. Very easy to fabricate in almost any shape, weather proof and properly built just about the lightest and most economical method out there. And with decent finishing skills, very slick.