You know there is so much controversy on this subject! I don't know if it effects inverter machines or not. My Lincoln V350-Pro has a carbon arc mode. But I won't use it for that! Years ago there was a discussion about this on the Miller site, one of the Miller reps jumped in and said there was no proof carbon arcing damaged a machine. I've personally seen it, and other very experienced weldors disagreed too! When I worked in a fab shop in the 1970s we had a dedicated electric Lincoln machine for carbon arcing. I had run 3/8 and 1/2-inch carbon arc rods with it. Also welded with it, it welded like crap! But I had used others machines of this type before and they welded beautifully. I have seen engine drives both Miller and Lincoln who had steady diets of carbon arcing, and they welded like crap too. I've never seen it, but have heard from other weldors where they seen the cranks in engine drives broke from carbon arcing.
Before you do it, I'd PM Mark with Everlast and ask his opinion. Mark is a very knowledgeable weldor!