Of course the model I showed was some kind of approximation to the case without balun or common mode choke on the feed line. With the balun you can expect better dipole symmetry, since it introduces high impedance to the current flowing into the coax.
One more observation from this model was that the antenna gain was reduced by about 3 dB, because the coax was conducting part of the RF current close to the lossy ground. To summarize you should use balun if you want to have ideal NVIS antenna with maximum antenna gain straight up. Otherwise it is not so important.