What would a polar plot or a Nyquist plot of an undamped second order system look like?
The Nyquist plot of a stable 2nd order TF looks like an 8-shaped balloon.
As the TF approaches &quot;undamped&quot;, the balloon grows and grows. There is no development of a sharp spike / pole as in a Bode plot.
The Nyquist plot of an undamped system has an infinite size balloon.
Here's an example of 3 systems with decreasing damping. (Ignore the H(s) expression at the top, it's the Matlab example. The TF vectors are what I entered based on your question)

In terms of errors, I think it depends how the engine handles the infinite magnitude and/or infinite re/im numbers. Matlab handles it quietly, Octave spits out errors. Both plot something resembling a horizontal line with the balloon curving back somewhere infinitely far away and out of screen.
Have a look here: https://www.mathworks.com/help/control/ref/nyquist.html