Depends on frequency, as the AM transmitter wavelength is hundreds of metres, so most of the pickup is via the wiring, whilst you will not get much just because you are so small that the transferred power is less than that you get from the light from the lamps.
It is true, but the allegedly dangerous power level limit "picked up" by the body is quite low, mainly on lower frequencies (with deep penetration). Higher frequencies are easier to pick up, but do no penetrate so deep, so affect only surface organs. And from these only eyes are sensitive (they are sensitive to temperature changes, but at the same time they do not have the blood flow to cool them down); There are known some skin burns, but these injuries originate from accidents, when wrong switch was used when switching off necessary antenna sections, so maintenance crew climbed directly on the energized section.
So if it is able to light the tubes with few meters of wire, the field is already quite high.
But on the other hand these unprotected areas are not the place, where operators stay majority of their shift, so the "dose level" they get would not be as high due to the short exposure time...