No, while they are grown in a cultured media, they are placed in a drop on a microscop slide. The zapper signal is applied theough an attenuating RC network so as to simulate the slide as being inside of the body. The signal is significantly reduced.
This roughly emulates the body's electrodynamics, excluding capacitances.
In this case, only 1.83 volts is applied across the slide and only at a few microamp current. Most of the current traves through the resistors, not the slide.