Brendan,
I don't think so. In recent interviews, Carlsen has asserted that he dislikes "classical chess" and has no interest in competing in the WC at that time control.
I get the impression MC's competing in the World Cup because it's one of the few tournaments he's never won. Commentators have suggested that, but I can't recall whether it was explicitly stated.
Being a cynic, I also wonder whether sponsorship or appearance money could be involved. 🤔