Drilled pearls are destroyed pearls from a scientific perspective. Much of the nuclear component is lost, making identification even more uncertain.
Interestingly enough though, by your description these are cultured pearls. "Devoid of anything" and "even and green" are disqualification points from the natural pearl side of the differential diagnosis. Likewise the absence of flame patterns demerit natural origin. Flame patterns are more typical in salt water pearls, hence these are likely fresh. Yet another demerit to natural origin, based upon the singular issue of availability (or lack of same).
Many strands, especially ones with no documentation or provenance claimed to be natural are not. Some are mixed strands. Many are elaborate fakes. Very, very few are unquestionably certifiable. Some are misunderstood through naivety, passed off as natural.
Like any pearl crafting, natural pieces are graded from pools of pearls. In almost every instance, compromises are made for the sake of inconsistencies. Symmetrical mismatching, as it were. Graduation by size, is technically that, as are color, surface and shape. Cultured pearls have eight grade points, naturals ten (add translucency and flame pattern). It's mathematically impossible to match a natural piece with the same scrutiny as cultured pieces... none more so than strands. Looking at this strand, it seems likely, nuclear clarity is co-incidental, as opposed to a point based in the selection criteria. Of thousands of natural pearls in my inventory, I'm often hard pressed to even find matched pairs. They truly are... like snow flakes.
Unless a natural strand is outrageously exceptional, the odds they'd have identical nuclei and florescence are astronomical.
Your hunch is reasonable. It's a beautiful strand, nonetheless.