I have corresponded with a lot of TLR guys who have removed the lid and/or opened up the airbox on the TLR.
On the 'busa, the airbox is upside down to what we have, on the TLR you can take the lid off and just have the air filter bolted above the v-twin throttle bodies.
BUT, I do know something about the effect of opening up the ram air system, and I have seen many dyno charts of our bikes with the lid off or modified.
The TLR loses about 3 to 5 hp at revs under 4000 (where our flappers open) but GAINS about 7 to 9 hp through midrange to up top, where it matters. On the TLR it is a tried and proven mod, and the dynos show that removing the lid or modifying the airbox give more gains than a full exhaust system - obviously most of us do both - good to have an R1 spanker...
Remember that Suzuki designed our TLRs to kill the superbike opposition, and the 'busa to have the nastiest engine EVER, but then had to "tame" them to the point where Joe Blow could ride around town (as his first bike?? ha ha!) - you get the point. That is why we get stuck with flapper valves, you don't think they are on any TLR/Busa race bikes do you??
Since the 'busa flappers open at 2500rpm you would only expect any losses below this figure, above 2500rpm only good things should happen from opening up the air flow...
The ram air theory has been kicked around the TLR sites for about a year, and what is generally accepted is that ram air does not need to be a perfect system. There are very noticable gains from having the increased flow of a modified intake system, and don't forget that many bikes have a non sealed airbox system like the RGV250.
As long as you pump lots of air into the system it will have greater then atmospheric pressure available at the throttle bodies. That is what counts. The turbulence from the convoluted path that the air must follow from the intakes can reduce the ram air effectiveness, and there are a couple of aftermarket air intake systems for the TLR that have better more curved passages, and we all remove the flappers and that crap plastic that gets in the way of air getting into our motors.
I predict that within a few months this site will be filled with stories of airbox mods and dyno charts showing easy 10+ hp gains from just cutting some plastic... Sorry about the long post guys.