the whine is a natural consequence of generating sound waves from the rotating wheels and all the complex periodic micro turbulances. The energy contained in those sound waves is, you are right, produced by the engine and as such are part of the "lost energy" so to speak. But those energy levels (contained in the sound waves themselves) are so small they are inconsequential. thus, direct efforts to reduce turbocharger whine itself are mis-applied as regards increasing the charger's efficiency.
In the stock intake tube, for example, there are some crafty characteristics designed to reduce sound emissions (they have to meet certain noise standards in order to sell the truck) but those devices don't necessarily improve turbocharger efficiency; they are designed to meet a federal noise requirement.
One observation I make is that the speed at which the essential mechanical events happen inside the turbo occur (for the higher power levels) are well above the highest frequency detected by (even young female) human hearing. So the audible components of those events must (I presume) occur from some complex sidebands or difference frequencies.
so in other words, (my opinion here) don't target the whine. embrace the whine
now then, there is an argument in favor of reducing turbulance, and such efforts, in my opinion, may be productive (even though none yet have been proven with statistical rigor to produce a repeatably measureable benefit). As a side effect, they may also reduce noise. So no, I would not strive to reduce it for its own sake. I would target turbulance and take the unintended consequence of sound reduction as a bonus.