Prince flirting with Orthodoxy?

Thanks to the pseudonymous Fr. Jape for calling my attention to this admittedly somewhat old news: "Is HRH the Prince of Wales considering entering the Orthodox Church?" Aside from the obvious constitutional implications of such a move, one wonders whether the Orthodox Church might have difficulties with a prospective convert publicly keeping a mistress. Would he have to follow his great-uncle's example by marrying and quitting the line of succession to the throne?