A little bit of circuit manipulation will indicate that yes, the comparator's noise contributes directly to the "input" noise, and therefore assists in meeting the criterion for oversampling. (One can imagine the comparator's input noise as a noise voltage source Vnoise in series with the ideal comparator's input; the voltage seen by the ideal comparator is then Vin + Vnoise).
One should not assume, however, that the comparator's noise is fully white; its spectrum is likely pink.