Now that we have a full look at the H2 it becomes much easier to discern what effect the aero bits will likely provide.
Downforce is out, structural support on the top winglets is minimal, if you've ever watched an F1 race and seen the close up slow mo's of the shimmy shaking aero pieces you'll know that no matter how strong the carbon is, air is abusive. Granted I'm no expert but support and surface area just do not seem robust enough to provide significant downforce at the front.
However, I do think the upper winglets are more about creating a smooth flow over the rider, working in combination with the fins on the tail section to create vortices that will clean up the turbulent air coming over the riders back (drag).
Its the wings on the lower part of the fairing that I find intriguing. From the looks they have been designed to create a Venturi Effect (reduction of pressure behind winglets). What this would do is greatly improve cooling. The decrease in pressure just fore of the rad vents would suck more hot air out. Without the winglets at speed that hot air runs up against a wall of air which blocks or diminishes heat dissipation (when it's most important, high revs, high speed). The winglets would eliminate that wall of air, instead creating a vacuum like effect.
The cooling angle is important for the H2-R. Heat kills engines, we've long known that, as a track only bike, the H2-R is going to see much of its life operating in high heat situations. This maximization of cooling is certainly going to help improve engine longevity.
This makes sense if you consider the Desmo GP10 which made use of similar winglets, in a similar place on a bike that was consistently running into heat soak problems (All Desmo's, not just the GP10)