"That doesn't matter, of course, since the technology to build such a device was non-existent during the Parthian period."
Well, the Persians built batteries but not "Crookes tubes"
The problem, with the Persian/Bagdhad cell is that it has no external cathode connection. My guess is that it wasn't a cell at all.
I keep my 2 feet on the ground, and my head in the twilight zone.