Certainly! You can see discrete emission lines from the ionized air molecules, which only occurs because of quantum physics. I realize that’s not what you’re asking though.

I did a quick calculation and for a plasma torch (~27000 Kelvin) and assuming air molecules, the average velocity of the plasma ions would only be like 6000 m/s. That’s 0.001% the speed of light, so you aren’t going to see any relativistic effects.