Plasmas do have different indices of refraction depending on their densities. This feature is used all the time in fusion research to... measure density. Microwaves are often the frequency of choice, though visible light can be used. There is a cutoff wavelength/frequency which is density dependent, past which the light is evanescent and does not propagate.
As far has having a transparent plasma that doesn't glow... could be difficult. The glow you usually see in a plasma comes from atoms that aren't fully ionized. In higher temperature plasmas, this occurs at the edge. If you had a fully ionized plasma, with impurities fully ionized as well, I would imagine that very little visible light would be emitted. Good luck actually constructing a system that can do that.