Although I have never seen this unit in the flesh, much less sampled it's effectiveness or otherwise, I am still trying to puzzle out what alleged mechanisms are at play within it.

The clues are there though; a closed/sealed room, reports of sinuses being affected and possibly headache inducing effects, the effect on a rising plume of smoke, the low voltage/low current draw, the blue light may have (but not a blue LED) all point to one likely candidate that might be responsible, but then the theory goes unstable when it's said the unit is totally sealed and the sound (not unlike sand) of rattling within the unit when shaken, but that might conceivably be part of a two stage process.  The blue LED I don't think is of any consequence beyond indicating that the device is active.  Are you sure it is an LED?  The device to test my theory costs more than this forum's collective spend on hi-fi toys, so it remains a theory

As for conducting objective measurements, I doubt if what I'm thinking along the lines of could be measured with a scope and multimeter.  The big problem with using those and/or a dB level meter is that the effects of for example cable changes rarely manifest themselves in an increase in sound levels and I don't know of any one electronic measuring device that can put a quantifiable value on "deeper soundstage, more presence, airier midrange, tigher more solid less boomy bass", etc., etc., which are all the adjectives us audiophools tend to apply to our successful tweaky type endeavours, because the ear/brain interface is considerably more sensitive and complex than a box of electronic measuring circuitry.