In fact, the actual function of the so-called Baghdad Battery is not known for certain. While it's possible that it was a primitive sort of galvanic cell, there are some reasons to believe otherwise. In any case, even if it were a battery, given the electrolytic chemicals available at the time the best that output that could have been expected from one would have been perhaps one-half to one volt, so it would have taken a whole hell of a lot of them to develop enough potential to power a Crookes Tube. That doesn't matter, of course, since the technology to build such a device was non-existent during the Parthian period.
http://news.bbc.co.uk/2/hi/science/nature/2804257.stm
http://en.wikipedia.org/wiki/Baghdad_Battery
http://archyfantasies.wordpress.com/...ghdad-battery/
ON EDIT: BTW, that thing shown in the photograph is not a Crookes Tube. It looks like a pretty standard neon tube with a fancy-shaped electrode to me.