Haha. Well if the charge generation is large enough (say, from the ferrocerium) then that shouldn't matter. I've seen it work with a small lump of (I think) Strontium-90.
Thinking about the tests described with a vacuum pulled in a closed LEC chamber, and the lack of measurable voltage between the two electrodes, then I guess that could be taken as evidence of the lack of electron generation in the tested WE.
However I always have, in the back of my mind, memories of a tale told to me in the 1980s by an old-timer who had been active in nuclear research since the 1940s, regarding the sometimes baffling behaviour of old electrical vacuum devices, which sometimes refused to do what was expected by theory...