Indeed you can go faster with a fairing. A couple years ago we had a loaner vintage Schwinn Paramount tandem set up for speed, big chain ring the size of a pie plate, Campy components and Phil Wood hubs front and rear. Probably around 1975 vintage bicycle and state of the art at that time. The bike owners had added a bubble fairing that Velcroed to the brake hoods and when both riders got into a tuck behind that fairing the bike was WICKED FAST!! It was way too much bike for us but we kept it for a year and did a few rides and had a little fun with it. Tires were 27 x 1 1/4 and that rear wheel was not easy to remove because of the curious design of the Phil Wood hub as I remember.
Land speed records are set with fairings. Not a gimmick.