We use density-functional theoretical methods to examine the recent prediction, based on a mean-field solution of the Zener model, that diamond doped by Mn (with spin S=5/2) would be a dilute magnetic semiconductor that remains ferromagnetic well above room temperature. Our findings suggest this to be unlikely, for four reasons: (1) substitutional Mn in diamond has a low-spin S=1/2 ground state; (2) the substitutional site is energetically unfavorable relative to the much larger "divacancy" site; 3) Mn in the divacancy site is an acceptor, but with only hyperdeep levels, and hence the holes are likely to remain localized; (4) the calculated Heisenberg couplings between Mn in nearby divacancy sites are two orders of magnitude smaller than for substitutional Mn in germanium.