If he was doing it for free it would be cool. It's sinking more money into a bike that will ride like ****, be a ***** to pick up and likely sour him on conversions that I have a problem with.
A varsity isn't completely worthless but paying $25+ for that frame would be a waste of money. Even if he can't get anything for the frame spending $25 on a converter is basically doing that. He would be far better off selling the frame for what he can and looking for something that is at least cromo.