I would have to be tested in a wind tunnel to be sure, but from reading books on racing car design, one of the worst aero drag areas is the boundry between the ground, and the underside of a vehicle. Anything smoothing that air helps.
Proof? I dont have any. Just acendotal evidence.
Mainly the look cool thing and maybe some wind protection, depends on the fairing. A long tail piece would make the biggest difference. It helps create a laminar flow around you and the bike. Imagine a falling rain drop. It isn't round but more of a tad-pole shape. The ratio of width to length is 1:7, ie 7 times longer than height to get a very good aerodynamic flow. The problem this ration make the bike unsafe in high winds. Take a look at Bonneville Salt Flat bikes and you'll see what I mean. A front full fairing vs naked actually add drag because a "burble" is formed behind the trailing edge of the fairing, creating negative pressure and in turn drag.
When I was racing bicycles I tried to be as aero as I could within rules and reason. It really does make a big difference when you only have about 3/4 of an hp to work with. Skin suit, aero rims and spokes, correct body position, shoes and shoe covers, helmet, etc.