You're presumably thinking that vaporised NaCl would consist of Na$^+$ and Cl$^-$ ions, but this isn't what you get. At temperatures just above the boiling point (1413c) you get neutral NaCl molecules and Na$_2$Cl$_2$ dimers, and possibly bigger polymers. Amazingly someone has measured this: see this paper for details (it's behind a paywall I'm afraid but you can see the abstract).
So the answer is no, the vapour is not a plasma. You'd have to heat it to much higher than the boiling point to get a plasma.
Electrically charged particles interact via their fields and so there is, in general, wide range interaction throughout the gas. The electromagnetic interactions between particles of the gas/plasma can give raise to effects which are significantly different from neutral gas, such as e.g waves. So to what extend the ideas gas law can be considered to "hold" for a plasma will depend on the parameters of the system, temperature, pressure, etc., but foremostly of the ionization degree of the gas/plasma.
It's an involved issue, as this quantity will depend on all the other parameters. One commonly cited relation for certain parameter ranges is the Saha equation, which relates temperature and particle density - which are both part of $PV=k_B T\cdot N$ too. Microscopic considerations in such a "chemical system", where the constituents can be ionized and thereby change their properties, lead you to the observation that the value charge density depends on the surroundings. So e.g. the Poission equation takes a nonlinear form $\Delta\Phi=\rho(\Phi)$.
It's then also related to new'ish system parameters like the Debye length, which caracterize the overall bahaviour you ask for. I'm sure there are Debye length-temperature ranges where it's perfectly reasonable to apply a gas law, just watch out which part of the system makes up charged particles or neutral ones. E.g. I think in space, there are a whole lot of charged particles, but people work with ideal gas laws.
A general rigourous classical look at it will lead you to $PV=k_B T\cdot \text{ln}(\mathcal Z)$, where the partition function contains the Hamiltonian of the system, which include the potentials $\Phi$ = energy expressions involving multiple variable-integrals over statistically weighted interaction potentials, see this link.
Best Answer
If the number of electrons and ions is exactly equal, it is still plasma. You are misunderstanding the quasineutrality requirement.
The term "plasma" was coined by Irving Langmuir with the phrase "We shall use the name plasma to describe this region containing balanced charges of ions and electrons", Oscillations in Ionized Gases Proc. Nat. Acad. Sci. U.S., vol. 14, p. 628, (1928)