Can't see the precious ones doing that.
No, you can't, but only because they will never be allowed the chance. Ask the Top Gear 'Star in a Reasonably Priced Car' Suzuki Liana what it was like having its wheels driven off by Lewis, Seb, Jenson et al.
Any of them would be pleased to do these sort of events if only a) the events still existed b) their employers allowed them to drive other cars and c) the F1 calendar had any gaps in it. Any current leading driver would be every bit as spectacular and committed as Hunt or whoever. Times may change but racers don't!