The obvious order parameter is something like the fraction of atoms or molecules ionized, say "x'. Simple stat mech says that at any finite temperature that will be in the range (0,1). The question is whether, for some density of particles, there's a discontinuity as a function of T in either x (first order) or dx/dT (second order). There's a reason some such discontinuity could happen. As more ions form, the Debye screening cloud lowers the free-energy of ion formation. That cooperative phenomenon, like many others, e.g. spin-spin interactions in magnets,can in principle lead to runaway feedback to a new phase. It's a quantitative question. A very quick first calculation indicates that unless the density of ions becomes larger than ~(kT/e^2)^3 (in cgs units), there won't be a phase transition. (Here k is Boltzmann's constant, T is temperature, and e is the ion charge.) Since x doesn't get large until T is pretty high, (Boltzmann factor), and since you don't have a gas to start with unless the overall concentration is pretty low, I think you typically don't get a phase transition. Somebody with more detailed knowledge should check that. Of course, the quantitative comparisons are completely different for say quark-gluon matter, etc.