Is conductivity equivalent to conductance per unit length?
I'd rather think of the units of conductivity as \$\dfrac{\mathrm{S}\cdot\mathrm{m}}{\mathrm{m}^2}\$. Which of course simplifies to S / m.

But what's really going on is that if the length of a conductor increases, the  conductance decreases, and if the cross sectional area increases the conductance increases. \$ G = \sigma A / l \$. Writing out the cancelled units tells more of the full story.


  PET has a conductivity on the order of 10−21 S/m; is this a valid value to use in this calculation? Or, is G a function of both the dielectric's conductance and the cable's geometry? If geometry is relevant, how?


This value is \$\sigma\$, the material conductivity, and not G from the characteristic impedance equation. But they are related.

In the characteristic impedance equation, you're interested in current conducted through the dielectric from the inner to the outer conductor. So the "length" dimension in the transmission line is one of the two "area" dimensions in the conductance equation. The other area dimension in a coaxial line would be some average of  circumference of the line (between the inner and outer conductor). The lenght dimension in the conductance equation would be the distance between the two conductors in the coax.

So 

\$ G_z = \dfrac{2\pi{}\bar{r}}{r_2 - r_1}\sigma\$

where Gz is the conductance per unit length needed for the characteristic impedance equation; r1 and r2 are the outer and inner conductor radii, and \$\bar{r}\$ is an "average" radius of the dielectric. I haven't thought through the correct way to take the average, but it would be whatever gives the correct overall conductance for a fixed length of line.