Have you ever tried cleaning rusty pitch shafts with oil? Does it work?
I’m guessing you might facilitate the removal of the outermost layer of rust with a little elbow grease and if a little fim was left on the shaft it wouldn’t rust as easily, but I don’t like the idea of sliding plastic gears onto an oily shaft. Also I think the shaft collars would absorb some oil and become stiff.
In other words I don’t think it is worth it. Just use a little steel wool.