The BPP super-tweeter cannot work, even in theory. Human hearing is a delicate instrument that positions the sounds according to how it enters the inner ear but also according to frequency of the sound. Lower frequency sounds have longer oscillating periods and this is the reason why we cannot always tell from where the sound is coming from. This is also the reason why usual placement of a subwoofer in a room makes little or no difference (generally speaking of course, there are always exceptions). On the other hand, high frequencies have shorter oscillating periods and it is quite easy to determine where the sound is coming from. This is also the reason why the usual placement of speakers should be so that the tweeter is in line with your ears (again, there are exceptions). In other words, unless this super-tweeter (20kHz or above) is directed to your inner ear, you will not hear anything. As for it being directed to "the area around your head" is just silly. The bone structure in our face cannot sense these kind of frequencies and it takes a large moving mass (say a diaphragm) below some 30Hz to do that and even then the results would be inconclusive because there are parts of the body that are much softer than the human skull so it would be difficult to determine which part of the body is responsible. Don't waste your money.
I am actually quite surprised that any serious company would be selling "hot water" to headphone enthusiasts. Though 50 bucks wouldn't kill you, there are better ways to spend that money. If you feel you have an extra 50 bucks, donate to charity. It will certainly do a far greater good than this.
On the headphones... It is of interest why they chose to add an additional power transformer behind before the headphones. This could mean that the headphones drivers have a substantially lower impedance or it might be that the impedance is unstable so that the amplifier would need to have a lower output impedance. Does anyone know the specifications for those headphones?