Given the drag at the speeds targeted, the lid off would have a massive effect.
Not necessarily as bad as you might think. Many years ago, Miles Kinsbury, with his Kingcycles, found that having a nose and a tail fairing on the bicycles made a quite dramatic change, and you didn't need sides, the air tended to flow along the side of the bike anyway, and the tailpiece brought the flow cleanly back together again.
Now I'll admit that you will get an advantage from having the complete fairing, since at the high speeds even quite minor adjustments to fairings can have measurable effects. I have my doubts that this alone will give him another 20mph however.